SOUTHDOWN INC
S-8, 1998-07-17
CEMENT, HYDRAULIC
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<PAGE>   1
 
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON JULY 17, 1998
 
                                           REGISTRATION NO. 333-
- --------------------------------------------------------------------------------
- --------------------------------------------------------------------------------
 
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                             ---------------------
                                    FORM S-8
 
                             REGISTRATION STATEMENT
                                     UNDER
                           THE SECURITIES ACT OF 1933
                             ---------------------
                                SOUTHDOWN, INC.
             (Exact name of registrant as specified in its charter)
 
<TABLE>
<S>                                            <C>
                  LOUISIANA                                      72-0296500
       (State or other jurisdiction of                        (I.R.S. Employer
        incorporation or organization)                      Identification No.)
        1200 SMITH STREET, SUITE 2400                              77002
                HOUSTON, TEXAS                                   (Zip Code)
   (Address of Principal Executive Offices)
               SOUTHDOWN, INC.                               MEDUSA CORPORATION
            1989 STOCK OPTION PLAN                     1991 LONG-TERM INCENTIVE PLAN
             (Full title of plan)                           (Full title of plan)
</TABLE>
 
                               PATRICK S. BULLARD
                VICE PRESIDENT -- GENERAL COUNSEL AND SECRETARY
                                SOUTHDOWN, INC.
                         1200 SMITH STREET, SUITE 2400
                              HOUSTON, TEXAS 77002
                    (Name and address of agent for service)
 
                                 (713) 650-6200
         (Telephone number, including area code, of agent for service)
                             ---------------------
                        CALCULATION OF REGISTRATION FEE
 
<TABLE>
<CAPTION>
- ------------------------------------------------------------------------------------------------------------------
- ------------------------------------------------------------------------------------------------------------------
                                                     PROPOSED MAXIMUM      PROPOSED MAXIMUM
  TITLE OF SECURITIES          AMOUNT TO BE           OFFERING PRICE      AGGREGATE OFFERING        AMOUNT OF
    TO BE REGISTERED            REGISTERED              PER SHARE               PRICE           REGISTRATION FEE
- ------------------------------------------------------------------------------------------------------------------
<S>                      <C>                       <C>                  <C>                    <C>
Common Stock, $1.25 par
value(1)................  3,000,000 shares(2)(3)       $70.5315(4)         $211,594,500(4)         $62,421(2)
- ------------------------------------------------------------------------------------------------------------------
Common Stock $1.25 par
  value(1)..............       521,752(3)(5)           $70.5315(4)         $ 36,799,952(4)           $10,856
- ------------------------------------------------------------------------------------------------------------------
          Total.........    3,521,752 shares(3)        $70.5315(4)         $248,394,452(4)         $73,277(2)
- ------------------------------------------------------------------------------------------------------------------
- ------------------------------------------------------------------------------------------------------------------
</TABLE>
 
(1) Includes the Preferred Stock Purchase Rights issuable pursuant to the Rights
    Agreement dated as of March 4, 1991, between the Registrant and ChaseMellon
    Shareholder Services, Inc. As no separate consideration is payable with
    respect to the Preferred Stock Purchase Rights, the registration fee with
    respect to such securities is included in the registration fee for the
    Common Stock.
 
(2) The 3,000,000 shares are in addition to the 2,000,000 shares initially
    available under the Southdown, Inc. 1989 Stock Option Plan which have been
    previously registered under the Securities Act of 1933, as amended (the
    "Securities Act") pursuant to the registration statement referred to in the
    final paragraph on this facing page, 252,895 of which shares have not yet
    been issued. A filing fee of $1,835.42 was previously paid by registrant
    with respect to such 252,895 shares.
 
(3) Pursuant to Rule 416 under the Securities Act, includes any additional
    shares issued pursuant to the antidilution provisions of the plan.
 
(4) Estimated solely for the purpose of determining the registration fee and
    calculated pursuant to Rule 457(c) and (h) by reference to the average of
    the high and low sales prices of the Common Stock on the New York Stock
    Exchange on July 15, 1998, which was $70.5315 per share.
 
(5) The 521,752 shares of Common Stock are issuable under the Medusa Corporation
    1991 Long-Term Incentive Plan, which was adopted by Southdown, Inc. in
    connection with the merger of a wholly-owned subsidiary of Southdown, Inc.
    into Medusa Corporation on June 30, 1998, pursuant to which Medusa
    Corporation became a wholly-owned subsidiary of Southdown, Inc.
 
     THE DOCUMENTS SENT OR GIVEN TO EMPLOYEES IN CONNECTION WITH THE SOUTHDOWN,
INC. 1989 STOCK OPTION PLAN AS DESCRIBED IN PART I OF THIS REGISTRATION
STATEMENT AND THE OTHER DOCUMENTS WHICH TOGETHER THEREWITH CONSTITUTE THE
PROSPECTUS MEETING THE REQUIREMENTS OF SECTION 10(A) OF THE SECURITIES ACT
CONSTITUTE, PURSUANT TO RULE 429 UNDER THE SECURITIES ACT, A COMBINED PROSPECTUS
THAT ALSO RELATES TO 252,895 SHARES OF COMMON STOCK REGISTERED ON FORM S-8,
REGISTRATION NO. 33-35011, WHICH BECAME EFFECTIVE ON JUNE 15, 1990.
- --------------------------------------------------------------------------------
- --------------------------------------------------------------------------------
<PAGE>   2
 
                                     PART I
 
              INFORMATION REQUIRED IN THE SECTION 10(A) PROSPECTUS
 
     The documents containing the information specified in Part I will be sent
or given to employees as specified by Rule 428(b). In accordance with the
instructions to Part I of Form S-8, such documents are not being filed and will
not be filed with the Securities and Exchange Commission (the "Commission"),
either as part of this registration statement or as a prospectus or prospectus
supplement pursuant to Rule 424.
 
                                    PART II
 
               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT
 
ITEM 3. INCORPORATION OF DOCUMENTS BY REFERENCE.
 
     The following documents, or portions of documents, previously filed by
Southdown, Inc. (the "Company") with the Commission are hereby incorporated
herein by reference:
 
          (a)  The Company's Annual Report on Form 10-K for the year ended
     December 31, 1997, as amended by Form 10-K/A filed on April 27, 1998;
 
          (b)  The Company's Quarterly Report on Form 10-Q for the quarter ended
     March 31, 1998;
 
          (c)  The Company's Current Report on Form 8-K filed on March 18, 1998,
     as amended by Form 8-K/A filed on April 10, 1998;
 
          (d)  The Company's Current Report on Form 8-K filed on June 18, 1998;
 
          (e)  The Company's Current Report on Form 8-K filed on July 15, 1998;
     and
 
          (f)  The Company's Registration Statement on Form 8-C relating to the
     Company's Common Stock and its Registration Statement on Form 8-A relating
     to the Company's Preferred Stock Purchase Rights, each as amended to date.
 
     All reports and other documents filed by the Company with the Commission
pursuant to Sections 13(a), 13(c), 14 and 15(d) of the Securities Exchange Act
of 1934, as amended, after the date of this Registration Statement and prior to
the termination of the offering of securities made hereby shall be deemed to be
incorporated by reference herein and to be a part hereof from the respective
dates of filing of such reports and other documents, other than the portions of
such documents which by statute, by designation in such documents or otherwise
are not required to be filed with the Commission or are not required to be
incorporated herein by reference. Any statement contained herein or in a
document incorporated or deemed to be incorporated by reference herein shall be
deemed to be modified or superseded for all purposes to the extent that a
statement contained in any other subsequently filed document that is also
incorporated or deemed to be incorporated by reference herein modifies or
supersedes such statement. Any such statement so modified or superseded shall
not be deemed, except as so modified or superseded, to constitute a part of this
Registration Statement.
 
ITEM 4. DESCRIPTION OF SECURITIES.
 
     Not applicable.
 
ITEM 5. INTERESTS OF NAMED EXPERTS AND COUNSEL.
 
     Not applicable.
 
ITEM 6. INDEMNIFICATION OF DIRECTORS AND OFFICERS.
 
     The Louisiana Business Corporation Law ("LBCL") generally gives a
corporation the power to indemnify any of its directors or officers against
certain expenses, judgments, fines and amounts paid in
 
                                        2
<PAGE>   3
 
settlement in connection with certain actions, suits or proceedings, provided
generally that such person acted in good faith and in a manner he reasonably
believed to be in or not opposed to the interests of the corporation and, with
respect to any criminal action or proceeding, had no reasonable cause to believe
his conduct was unlawful. In the case of an action by, or in the right of, the
corporation, the corporation may indemnify such person against expenses,
including attorneys' fees and amounts paid in settlement not exceeding, in the
judgment of the board of directors, the estimated expense of litigating the
action to conclusion, actually and reasonably incurred in connection with the
defense or settlement of such action, and no indemnification shall be made in
respect of any claim, issue, or matter as to which such person shall have been
adjudged by a court of competent jurisdiction, after exhaustion of all appeals
therefrom, to be liable for willful or intentional misconduct in the performance
of his duty to the corporation, unless, and only to the extent that the court
shall determine upon application that, despite the adjudication of liability but
in view of all the circumstances of the case, he is fairly and reasonably
entitled to indemnity for such expenses which the court shall deem proper.
 
     Indemnification provided pursuant to the foregoing provisions is not, under
the LBCL, deemed exclusive of any other rights to which the person indemnified
is entitled under any bylaw, agreement, authorization of shareholders or
directors; however, no such other indemnification measure shall permit
indemnification of any person for the results of such person's willful or
intentional misconduct. In addition, the LBCL contains provisions to the general
effect that any director shall in the performance of his duties be fully
protected in relying in good faith upon the records of the corporation and upon
such information, opinions, reports or statements presented to the corporation,
the board of directors, or any committee thereof by any of the corporation's
officers or employees, or by any committee of the board of directors, or by any
counsel, appraiser, engineer (including a petroleum reservoir engineer), or
independent or certified public accountant selected by the board of directors or
any committee thereof with reasonable care, or by any other person as to matters
the director reasonably believes are within such other person's professional or
expert competence and which person is selected by the board of directors or any
committee thereof with reasonable care. A director shall not be liable for the
commission of a prohibited act if his dissent was either noted in the minutes of
the meetings or filed promptly thereafter in the registered office of the
corporation.
 
     As permitted under Section 24(C)(4) of the LBCL, Article XIII of the
Restated Articles of Incorporation of the Company eliminates the personal
liability of any director or officer to the Company or its shareholders for
monetary damages for breach of fiduciary duty in such capacity, except for (i)
any breach of the duty of loyalty to the Company or its shareholders; (ii) acts
or omissions not in good faith or involving intentional misconduct or a knowing
violation of law; (iii) unlawful payment of dividends or unlawful stock purchase
or redemption; or (iv) any transaction from which the director or officer
derived an improper personal benefit.
 
     Article VI, Section 6 of the Company's Bylaws contemplates that the Company
shall indemnify its directors and officers to the maximum extent permitted by
Louisiana law.
 
     In addition, the Company has purchased a liability insurance policy under
which its directors and officers are indemnified against certain losses arising
from certain claims that may be made against them by reason of their serving in
such capacity.
 
ITEM 7. EXEMPTION FROM REGISTRATION CLAIMED.
 
     Not applicable.
 
                                        3
<PAGE>   4
 
ITEM 8. EXHIBITS.
 
<TABLE>
<CAPTION>
      EXHIBIT NO.                                DESCRIPTION
      -----------                                -----------
<C>                      <S>
          3.1            -- Restated Articles of Incorporation of the Registrant, as
                            amended through July 17, 1998.
          3.2            -- Bylaws of the Registrant, amended as of July 1, 1998.
          4.1*           -- 1989 Stock Option Plan of Registrant, as
                            amended -- incorporated by reference from Exhibit 10.2 to
                            the Registrant's Registration Statement on Form S-4
                            (Registration No. 333-49161).
          4.2*           -- Medusa Corporation 1991 Long-Term Incentive
                            Plan -- incorporated by reference from Exhibit 4.3 to
                            Medusa Corporation's Registration Statement on Form S-8
                            (Registration No. 33-45182) filed with the Commission on
                            February 20, 1996.
          5              -- Opinions of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Weiss Walmsley & Casteix, L.L.P.
                            regarding the legality of the shares of Common Stock
                            covered by this Registration Statement.
         15              -- Letter of Deloitte & Touche LLP regarding unaudited
                            interim financial information.
         23.1            -- Consents of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Weiss Walmsley & Casteix, L.L.P.
                            (included in their opinion filed as Exhibit 5 hereto).
         23.2            -- Consent of Deloitte & Touche LLP.
</TABLE>
 
- ---------------
 
* Incorporated by reference
 
ITEM 9. UNDERTAKINGS.
 
     (a) The undersigned registrant hereby undertakes:
 
          (1) To file, during any period in which offers or sales are being
     made, a post-effective amendment to this registration statement:
 
             (i) To include any prospectus required by section 10(a)(3) of the
        Securities Act of 1933 (the "Securities Act");
 
             (ii) To reflect in the prospectus any facts or events arising after
        the effective date of the registration statement (or the most recent
        post-effective amendment thereof) which, individually or in the
        aggregate, represent a fundamental change in the information set forth
        in the registration statement;
 
             (iii) To include any material information with respect to the plan
        of distribution not previously disclosed in the registration statement
        or any material change to such information in the registration
        statement;
 
     Provided, however, that paragraphs (a)(1)(i) and (a)(1)(ii) above shall not
     apply if the information required to be included in a post-effective
     amendment by those paragraphs is contained in periodic reports filed with
     or furnished to the Commission by the registrant pursuant to Section 13 or
     Section 15(d) of the Securities Exchange Act of 1934 (the "Exchange Act")
     that are incorporated by reference in this Registration Statement.
 
          (2) That, for the purpose of determining any liability under the
     Securities Act, each such post-effective amendment shall be deemed to be a
     new registration statement relating to the securities offered therein, and
     the offering of such securities at that time shall be deemed to be the
     initial bona fide offering thereof.
 
                                        4
<PAGE>   5
 
          (3) To remove from registration by means of a post-effective amendment
     any of the securities being registered which remain unsold at the
     termination of the offering.
 
     (b) The undersigned registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act, each filing of the
registrant's annual report pursuant to section 13(a) or section 15(d) of the
Exchange Act that is incorporated by reference in the registration statement
shall be deemed to be a new registration statement relating to the securities
offered therein, and the offering of such securities at that time shall be
deemed to be the initial bona fide offering thereof.
 
     (c) Insofar as indemnification for liabilities arising under the Securities
Act may be permitted to directors, officers and controlling persons of the
registrant pursuant to the foregoing provisions, or otherwise, the registrant
has been advised that in the opinion of the Securities and Exchange Commission
such indemnification is against public policy as expressed in the Securities Act
and is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment by the registrant of expenses
incurred or paid by a director, officer or controlling person of the registrant
in the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Securities Act and will be governed by the final
adjudication of such issue.
 
                                        5
<PAGE>   6
 
                                   SIGNATURES
 
     Pursuant to the requirements of the Securities Act of 1933, the registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Houston, State of Texas, on the 17th day of July,
1998.
 
                                            SOUTHDOWN, INC.
 
                                            By:    /s/ CLARENCE C. COMER
                                              ----------------------------------
                                                      Clarence C. Comer
                                                President and Chief Executive
                                                            Officer
 
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated.
 
<TABLE>
<CAPTION>
                      SIGNATURE                                       TITLE                        DATE
                      ---------                                       -----                        ----
<C>                                                     <S>                                <C>
 
                /s/ CLARENCE C. COMER                   President and Chief Executive         July 17, 1998
- -----------------------------------------------------     Officer and Director (Principal
                  Clarence C. Comer                       Executive Officer)
 
                 /s/ DENNIS M. THIES                    Executive Vice President --           July 17, 1998
- -----------------------------------------------------     Finance and Chief Financial
                   Dennis M. Thies                        Officer (Principal Financial
                                                          Officer)
 
                /s/ ALLAN B. KORSAKOV                   Vice President and Corporate          July 17, 1998
- -----------------------------------------------------     Controller (Principal Accounting
                  Allan B. Korsakov                       Officer)
 
                   /s/ R. S. EVANS                      Director                              July 17, 1998
- -----------------------------------------------------
                     R. S. Evans
 
              /s/ KILLIAN L. HUGER, JR.                 Director                              July 17, 1998
- -----------------------------------------------------
                Killian L. Huger, Jr.
 
                /s/ ROBERT G. POTTER                    Director                              July 17, 1998
- -----------------------------------------------------
                  Robert G. Potter
 
                  /s/ FRANK J. RYAN                     Director                              July 17, 1998
- -----------------------------------------------------
                    Frank J. Ryan
 
                 /s/ WHITSON SADLER                     Director                              July 17, 1998
- -----------------------------------------------------
                   Whitson Sadler
 
                /s/ ROBERT J. SLATER                    Director                              July 17, 1998
- -----------------------------------------------------
                  Robert J. Slater
</TABLE>
 
                                        6
<PAGE>   7
 
<TABLE>
<CAPTION>
                      SIGNATURE                                       TITLE                        DATE
                      ---------                                       -----                        ----
<C>                                                     <S>                                <C>
 
              /s/ DAVID J. TIPPECONNIC                  Director                              July 17, 1998
- -----------------------------------------------------
                David J. Tippeconnic
 
                /s/ J. BRUCE TOMPKINS                   Director                              July 17, 1998
- -----------------------------------------------------
                  J. Bruce Tompkins
 
              /s/ GEORGE E. UDING, JR.                  Director                              July 17, 1998
- -----------------------------------------------------
                George E. Uding, Jr.
 
               /s/ V. H. VAN HORN, III                  Director                              July 17, 1998
- -----------------------------------------------------
                 V. H. Van Horn, III
 
               /s/ STEVEN B. WOLITZER                   Director                              July 17, 1998
- -----------------------------------------------------
                 Steven B. Wolitzer
</TABLE>
 
                                        7
<PAGE>   8
 
                                 EXHIBIT INDEX
 
<TABLE>
<CAPTION>
      EXHIBIT NO.                                DESCRIPTION
      -----------                                -----------
<C>                      <S>
 
          3.1            -- Restated Articles of Incorporation of the Registrant, as
                            amended through July 17, 1998.
          3.2            -- Bylaws of the Registrant, amended as of July 1, 1998.
          4.1*           -- 1989 Stock Option Plan of Registrant, as
                            amended -- incorporated by reference from Exhibit 10.2 to
                            the Registrant's Registration Statement on Form S-4
                            (Registration No. 333-49161).
          4.2*           -- Medusa Corporation 1991 Long-Term Incentive
                            Plan -- incorporated by reference from Exhibit 4.3 to
                            Medusa Corporation's Registration Statement on Form S-8
                            (Registration No. 33-45182) filed with the Commission on
                            February 20, 1996.
          5              -- Opinions of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Weiss Walmsley & Casteix, L.L.P.
                            regarding the legality of the shares of Common Stock
                            covered by this Registration Statement.
         15              -- Letter of Deloitte & Touche LLP regarding unaudited
                            interim financial information.
         23.1            -- Consents of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Weiss Walmsley & Casteix, L.L.P.
                            (included in their opinion filed as Exhibit 5 hereto).
         23.2            -- Consent of Deloitte & Touche LLP.
</TABLE>
 
- ---------------
 
* Incorporated by reference
 
                                        8

<PAGE>   1
 
                                                                     EXHIBIT 3.1
 
                       RESTATED ARTICLES OF INCORPORATION
                                       OF
                                SOUTHDOWN, INC.
 
     Southdown, Inc., a Louisiana corporation (the "corporation"), through its
undersigned President and Secretary and by authority of its Board of Directors,
does hereby certify that:
 
     FIRST: The Restated Articles of Incorporation set forth in Paragraph Fourth
below accurately copies the articles and all amendments and corrections thereto
in effect at the date hereof without any substantive changes.
 
     SECOND: Each amendment and correction has been effected in conformity with
law.
 
     THIRD: The date of incorporation of the corporation was April 4, 1930, and
the date of these Restated Articles is September 15, 1983.
 
     FOURTH: The Restated Articles of Incorporation of the corporation are as
follows:
 
                                   ARTICLE I
 
     The name of this corporation shall be Southdown, Inc.
 
                                   ARTICLE II
 
     The corporation's purpose is to engage in any lawful activity for which
corporations may be formed under the Business Corporation Law of Louisiana.
 
                                  ARTICLE III
 
     A. The Corporation has authority to issue 20,000,000 shares of Common Stock
of the par value of $2.50 per share (the "Common Stock") and 5,000,000 shares of
Preferred Stock of the par value of $0.10 per share (the "Preferred Stock").
 
     B. Shares of the Preferred Stock may be issued from time to time in one or
more classes or series, each of which shall have such distinctive designation or
title and such voting rights, preferences and relative, optional or other
special rights (including, without limitation, pre-emptive rights) and
qualifications, limitations or restrictions as shall be fixed by the board of
directors of the corporation prior to the issuance of any shares thereof by
amendment to these Articles of Incorporation adopted by the board of directors.
 
     C. Except to the extent otherwise provided by an amendment adopted by the
board of directors in accordance with the provisions of Article III (B) hereof,
no shareholder of this corporation shall by reason of his holding shares of any
class have any pre-emptive or preferential right to purchase or subscribe to any
shares of any class of this corporation now or hereafter authorized or any
notes, debentures, bonds or other securities convertible into or carrying
options or warrants to purchase shares of any class now or hereafter to be
authorized, whether or not the issuance of any shares, or such notes,
debentures, bonds, or other securities would adversely affect dividend or voting
rights of such shareholder, other than such rights, if any, as the board of
directors in its discretion may fix; and the board of directors may issue shares
of any class of this corporation, or any notes, debentures, bonds or other
securities convertible into or carrying options or warrants to purchase shares
of any class, without offering any such shares of any class, either in whole or
in part, to the existing shareholders of any class.
<PAGE>   2
 
                                   ARTICLE IV
 
     All of the corporate powers of this corporation shall be vested in and
exercised by a board of directors consisting of the number of directors
specified in the by-laws of the corporation or determined in the manner
prescribed herein.
 
     The Board of Directors shall be divided into three classes as nearly equal
in number as may be, with the initial term of office of Class I expiring at the
annual meeting of shareholders in 1971, of Class II expiring at the annual
meeting of shareholders in 1972, and of Class III expiring at the annual meeting
of shareholders in 1973.
 
     At each annual meeting of shareholders, directors chosen to succeed those
whose terms then expire shall be elected for a full term of office expiring at
the third succeeding annual meeting of shareholders after their election. When
the number of directors is increased by amendment to the by-laws of the
corporation, and any newly created directorships are filled by the Board of
Directors, there shall be no classification of such additional directors until
the next annual meeting of shareholders. Subject to the foregoing, directors
elected to fill a vacancy shall hold office for a term expiring at the annual
meeting at which the term of the class to which they shall have been elected
expires.
 
     The shareholders, by the affirmative vote or consent of the holders of 80%
of all classes of stock of this corporation entitled to vote in elections of
directors, at any special meeting called for the purpose may remove from office
any one or more of the directors, notwithstanding that his or their terms of
office may not have expired, and may forthwith at such meeting proceed to elect
a successor for the unexpired term.
 
                                   ARTICLE V
 
     Any director absent from the meeting of the board of directors or any
committee thereof may be represented by any other director or shareholder, who
may cast the absent director's vote according to his written instructions,
general or special.
 
                                   ARTICLE VI
 
     The board of directors may make and alter by-laws containing any provisions
with respect to the government of the corporation, subject to the power of the
shareholders to change or repeal any by-laws so made. The by-laws may contain
any provision relating to the business of the corporation, the conduct of its
affairs, its rights or powers, or the rights or powers of its shareholders,
directors or officers, not inconsistent with law or these articles.
 
                                  ARTICLE VII
 
     No shareholder shall ever be held liable for the contracts, faults or debts
of the corporation in any further sum than the unpaid balance, if any, remaining
due on the stock for which he has subscribed, nor shall any informality in
organization have the effect of rendering any subscriber or shareholder liable
beyond the said unpaid amount, if any, remaining due on his stock.
 
                                  ARTICLE VIII
 
     Notwithstanding any other provision of this certificate of incorporation or
the by-laws of this corporation (and in addition to any other vote that may be
required by law, the Articles of Incorporation or the by-laws of this
corporation), the affirmative vote of the holders of 80% of all classes of stock
of this Corporation entitled to vote in elections of directors (considered for
this purpose as one class) shall be required to amend, alter, change, or repeal
Articles IV, VIII, VI, IX, X or XI of the Articles of Incorporation.
 
     Except as provided in the Articles of Incorporation, or as required by
statute, the Articles of Incorporation may be amended by the affirmative vote or
consent of the holders of a majority of all classes of
 
                                        2
<PAGE>   3
 
stock of this corporation entitled to vote in elections of directors, taken at
an annual or special meeting of shareholders, the notice of which set forth the
proposed amendment or a summary of the changes to be made thereby. If such an
amendment would adversely affect the holders of shares of any class or series,
then in addition to the vote required by the sentence immediately preceding, the
holders of each class or series of shares so affected by the amendment shall be
entitled to vote as a class upon such amendment, and a majority of the issued
and outstanding shares of each class or series so affected by the amendment
shall be necessary to the adoption thereof.
 
                                   ARTICLE IX
 
     (A) Except as set forth in Paragraph (D) of this Article IX, the
affirmative vote or consent of the holders of 80% of all classes of stock of
this corporation entitled to vote in elections of directors, considered for the
purposes of this Article IX as one class, shall be required:
 
          (i) for a merger or consolidation with or into any other corporation,
     or
 
          (ii) for any sale or lease of all or any substantial part of the
     assets of this corporation to any other corporation, person or other
     entity, or
 
          (iii) any sale or lease to this corporation or any subsidiary thereof
     of any assets (except assets having an aggregate fair market value of less
     than $2,000,000) in exchange for voting securities (or securities
     convertible into voting securities or options, warrants, or rights to
     purchase voting securities or securities convertible into voting
     securities) of this corporation or any subsidiary by any other corporation,
     person or entity,
 
if as of the record date for the determination of shareholders entitled to
notice thereof and to vote thereon or consent thereto such other corporation,
person or entity which is party to such a transaction is the beneficial owner,
directly or indirectly, of 5% or more of the outstanding shares of stock of this
corporation entitled to vote in elections of directors, considered for the
purpose of this Article IX as one class. Such affirmative vote or consent shall
be in addition to the vote or consent of the holders of the stock of this
corporation otherwise required by law or any agreement between this corporation
and any national securities exchange.
 
     (B) For purposes of this Article IX any corporation, person or other entity
shall be deemed to be the beneficial owner of any share of stock of this
corporation,
 
          (i) which it owns directly, whether or not of record, or
 
          (ii) which it has the right to acquire pursuant to any agreement or
     understanding or upon exercise of conversion rights, warrants or options or
     otherwise, or
 
          (iii) which are beneficially owned, directly or indirectly (including
     shares deemed to be owned through application of clause (ii) above), by any
     "affiliate" or "associate" as those terms are defined in Rule 12b-2 of the
     General Rules and Regulations under the Securities Exchange Act of 1934 as
     in effect on July 1, 1970, or
 
          (iv) which are beneficially owned, directly or indirectly (including
     shares deemed owned through application of clause (ii) above), by any other
     corporation, person or entity with which it or its "affiliate" or
     "associate" has any agreement or arrangement or understanding for the
     purpose of acquiring, holding, voting or disposing of stock of this
     corporation.
 
     For the purposes of this Article IX, the outstanding shares of any class of
stock of this corporation shall include shares deemed owned through the
application of clauses (B)(ii), (iii) and (iv) above, but shall not include any
other shares which may be issuable pursuant to any agreement or upon exercise of
conversion rights, warrants, options or otherwise.
 
                                        3
<PAGE>   4
 
     (C) The Board of Directors shall have the power and duty to determine for
the purposes of this Article IX on the basis of information known to this
corporation, whether
 
          (i) such other corporation, person or other entity beneficially owns
     more than 5% of the outstanding shares of stock of this corporation
     entitled to vote in elections of directors,
 
          (ii) a corporation, person, or entity is an "affiliate" or "associate"
     (as defined in Paragraph (B) above) of another,
 
          (iii) the assets being acquired by this corporation, or any subsidiary
     thereof, have an aggregate fair market value of less than $2,000,000 and
 
          (iv) the memorandum of understanding referred to in paragraph (D)
     below is substantially consistent with the transaction covered thereby.
 
     Any such determination shall be conclusive and binding for all purposes of
this Article IX.
 
     (D) The provisions of this Article IX shall not apply to,
 
          (i) any merger or similar transaction with any corporation if the
     Board of Directors of this corporation has approved a memorandum of
     understanding with such other corporation with respect to such transaction
     prior to the time that such other corporation shall have become a
     beneficial owner of more than 5% of the outstanding shares of stock of this
     corporation entitled to vote in elections of directors; or
 
          (ii) any merger or consolidation of this corporation with, or any sale
     or lease to this corporation or any subsidiary thereof of any assets of or
     sale or lease by this corporation or any subsidiary thereof of any its
     assets to (a) any corporation of which a majority of the outstanding shares
     of all classes of stock entitled to vote in elections of directors is owned
     of record or beneficially by this corporation and its subsidiaries or (b)
     Zapata Norness Incorporated, a Delaware corporation, or any successor,
     affiliate, associate or subsidiary.
 
     (E) Except as may be otherwise provided by this Article IX or required by
statute, an agreement of merger or consolidation may be approved by a majority
vote of the shares issued and outstanding, taker at a meeting called for the
purpose of such approval.
 
                                   ARTICLE X
 
     Special meetings of shareholders may be called by 80% or more of the Board
of Directors or of the Executive Committee thereof or the President of this
corporation and shall be called upon the written request of the holders of 80%
or more of this corporation's stock outstanding and entitled to vote for
directors as of the date of such request.
 
                                   ARTICLE XI
 
     In furtherance and not in limitation of the powers conferred by statute,
the Board of Directors is expressly authorized to make, alter or repeal the
by-laws of the corporation by the affirmative vote of 80% of the entire Board of
Directors. Such by-laws may be adopted, amended or repealed by the affirmative
vote of the holders of 80% of this corporation's stock outstanding and entitled
to vote at the meeting at which any by-law is adopted, amended or repealed. To
the extent not determined by the Articles of Incorporation, the number,
qualification, term of office, manner of election, time and place of meeting,
compensation and powers and duties of the directors may be prescribed from time
to time by the by-laws. The by-laws may contain any other provisions for the
regulation and management of the affairs of the corporation not inconsistent
with statute or the Articles of Incorporation.
 
                                        4
<PAGE>   5
 
                                  ARTICLE XII
 
     Cash, property or share dividends, shares issuable to shareholders in
connection with a reclassification of stock, and the redemption price of
redeemed shares of Preferred Stock, which are not claimed by the shareholders
entitled thereto within one year after the dividend or redemption price became
payable or the shares became issuable, despite reasonable efforts by the
corporation to pay the dividend or redemption price or deliver the certificates
for the shares to such shareholders within such time, shall, at the expiration
of such time, revert to full ownership to the corporation, and the corporation's
obligation to pay such dividend or redemption price or issue such shares, as the
case may be, shall thereupon cease; provided that the board of directors may, at
any time, for any reason satisfactory to it, but need not, authorize (a) payment
of the amount of any cash or property dividend or redemption price, or (b)
issuance of any shares, ownership of which has reverted to the corporation
pursuant to this Article XII, to the person or entity who or which would be
entitled thereto had such reversion not occurred.
 
Dated: September 15th, 1983
 
                                            SOUTHDOWN, INC.
 
                                            By:   /s/ LAURENCE E. HIRSCH
                                              ----------------------------------
                                                     Laurence E. Hirsch,
                                                          President
 
                                            By:     /s/ E. B. SCHERICH
                                              ----------------------------------
                                                       E. B. Scherich,
                                                          Secretary
 
                                        5
<PAGE>   6
 
                                 ACKNOWLEDGMENT
 
STATE OF TEXAS
 
COUNTY OF HARRIS
 
     BEFORE ME, the undersigned authority, personally came and appeared Laurence
E. Hirsch and E. B. Scherich to me known to be the President and Secretary of
Southdown, Inc. and the persons who executed the foregoing instrument in such
capacities, and who, being duly sworn, acknowledged in my presence and in the
presence of the undersigned witnesses that they were authorized to and did
execute the foregoing instrument in such capacities for the said corporation, as
its and their free act and deed.
 
     IN WITNESS WHEREOF, the appearers and witnesses and I have hereunto affixed
our signatures on this 15th day of September, 1983.
 
WITNESSES:
 
<TABLE>
<S>                                                    <C>
                /s/ MICHELLE RAYMOND                                  /s/ LAURENCE E. HIRSCH
- -----------------------------------------------------  -----------------------------------------------------
                  /s/ MARIE KALISEK                                     Laurence E. Hirsch,
- -----------------------------------------------------                        President
 
                /s/ MICHELLE RAYMOND                                    /s/ E. B. SCHERICH
- -----------------------------------------------------  -----------------------------------------------------
                  /s/ MARIE KALISEK                                       E. B. Scherich,
- -----------------------------------------------------                        Secretary
</TABLE>
 
                               /s/ DANA LLOYD
                       ----------------------------------
                                 NOTARY PUBLIC
 
                                 [Notary Seal]
<PAGE>   7
 
                            ARTICLES OF AMENDMENT TO
                       RESTATED ARTICLES OF INCORPORATION
                             DATED DECEMBER 2, 1987
 
<TABLE>
<S>                                             <C>           <C>
ARTICLES OF AMENDMENT TO                        sec.          UNITED STATES OF AMERICA
RESTATED ARTICLES OF                            sec.          STATE OF TEXAS
INCORPORATION OF                                sec.          COUNTY OF HARRIS
SOUTHDOWN, INC.                                 sec.
</TABLE>
 
     BE IT KNOWN, that on this 2nd day of December, 1987, BEFORE ME, Margaret
Bassett, a Notary Public, duly commissioned and qualified, in and for the County
of Harris, and in the presence of the witnesses hereinafter named and
undersigned:
 
                         PERSONALLY CAME AND APPEARED:
 
     CLARENCE C. COMER and WENDELL E. PHILLIPS, II, appearing herein and acting
for Southdown, Inc. (of which Corporation they are, respectively, President and
Secretary), a corporation organized and existing under the laws of the State of
Louisiana, domiciled in the Parish of Orleans, State of Louisiana, organized by
Articles of Incorporation executed and acknowledged on April 4, 1930, and
recorded on April 5, 1930 in the records of the Recorder of the Parish of
Orleans and on April 7, 1930, in the Record of Charters Book 130, who declared
that pursuant to resolution of the shareholders of the corporation, adopted at a
special meeting of shareholders of the corporation held on December 2, 1987, at
2:00 p.m., at the offices of the corporation, 1200 Smith Street, Suite 2200,
Houston, Texas, they now appear for the purpose of executing this act of
amendment and putting into authentic form the amendment so agreed to by the vote
of the shareholders of said corporation.
 
     AND THE SAID APPEARERS further declared that by vote of the shareholders of
the corporation, it was resolved that the Articles of Incorporated of the
corporation be amended by adding a new Article XIII as follows:
 
          "No director or officer of this corporation shall be personally liable
     to this corporation or its shareholders for monetary damages for breach of
     fiduciary duty as a director or officer, except for liability (i) for
     breach of the director's or officer's duty of loyalty to this corporation
     or its shareholders, (ii) for acts or omissions not in good faith or which
     involve intentional misconduct or a knowing violation of law, (iii) under
     Section 92(D) of the Louisiana Business Corporation Law, or (iv) for any
     transaction from which the director or officer derived an improper personal
     benefit. If the Louisiana Business Corporation Law is hereafter amended to
     authorize corporate action further limiting or eliminating the personal
     liability of directors or officers, then the liability of each director and
     officer of this corporation shall be limited or eliminated to the full
     extent permitted by the Louisiana Business Corporation Law as so amended
     from time to time. Neither the amendment nor repeal of this Article, nor
     the adoption of any provision of this corporation's Articles of
     Incorporation inconsistent with this Article, shall eliminate or reduce the
     effect of this Article, in respect of any matter occurring, or any cause of
     action, suit or claim that, but for this Article, would accrue or arise,
     prior to such amendment, repeal or adoption of any inconsistent provision."
 
     AND THE SAID APPEARERS further declared that 5,615,745 of the shares of the
corporation were represented at said meeting and that 5,214,882 shares voted for
the said amendment and that 400,863 shares voted against the said amendment.
 
     AND THE SAID APPEARERS having requested me, Notary, to note said amendment
in authentic form, I do by these presents receive said amendment in the form of
this public act to the end that said amendment may be promulgated and recorded
and thus be read into the original Restated Articles of Incorporation of
Southdown, Inc., as hereinabove set forth.
<PAGE>   8
 
     THUS DONE AND PASSED, in my office at Houston, Texas, on the day, month and
year first above written, in the presence of the undersigned competent
witnesses, who here unto sign their names with the said appearers and me,
Notary, after a due reading of the whole.
 
                                            SOUTHDOWN, INC.
 
                                            By:    /s/ CLARENCE C. COMER
                                              ----------------------------------
                                                      Clarence C. Comer
                                                          President
 
                                            By:   /s/ WENDELL E. PHILLIPS
                                              ----------------------------------
                                                   Wendell E. Phillips, II
                                                          Secretary
 
WITNESSES:
 
    /s/ EDGAR J. MARSTON III
- ------------------------------------
        Edgar J. Marston III
 
       /s/ DENNIS M. THIES
- ------------------------------------
          Dennis M. Thies
 
                            /s/ MARGARET BASSETT
             ------------------------------------------------------
                                 NOTARY PUBLIC
 
                                 [Notary Seal]
 
                                        2
<PAGE>   9
 
                            ARTICLES OF AMENDMENT TO
                       RESTATED ARTICLES OF INCORPORATION
                               DATED MAY 23, 1988
 
<TABLE>
<S>                                       <C>          <C>
ARTICLES OF AMENDMENT TO                  sec.         STATE OF TEXAS
RESTATED ARTICLES OF                      sec.         COUNTY OF HARRIS
INCORPORATION OF                          sec.         CITY OF HOUSTON
SOUTHDOWN, INC.                           sec.
</TABLE>
 
     BE IT KNOWN, That on this 23rd day of May, 1988,
 
     BEFORE ME, Shawna Chisnell, a Notary Public, duly commissioned and
qualified in and for the County of Harris, State of Texas, and in the presence
of the witnesses hereinafter named and undersigned:
 
                         PERSONALLY CAME AND APPEARED:
 
     EDGAR J. MARSTON III and WENDELL E. PHILLIPS, II, appearing herein and
acting for Southdown, Inc. (of which Corporation they are, respectively,
Executive Vice President and Secretary), a corporation organized and existing
under the laws of the State of Louisiana, domiciled in the Parish of Orleans,
State of Louisiana, organized by Articles of Incorporation effective April 4,
1930, which Articles, as amended, were restated pursuant to Restated Articles of
Incorporation effective September 15, 1983, who declared that pursuant to
resolutions of the shareholders of the Corporation adopted at an annual meeting
of the shareholders of the Corporation held on May 19, 1988 at 10:15 a.m., at
the Doubletree Hotel, 400 Dallas Street, Houston, Texas 77002, they now appear
for the purpose of executing this act of amendment and putting into authentic
form the amendment so agreed to by the shareholders of said Corporation, which
amendment shall become effective at 5:00 p.m., Central Daylight Savings Time, on
May 27, 1988.
 
     AND THE SAID APPEARERS further declare that by vote of the shareholders of
said Corporation, it was:
 
     RESOLVED, that Article III of the Restated Articles of Incorporation of
Southdown, Inc. be amended so that:
 
          (1) Paragraph A. is amended to read in its entirety as follows:
 
             The Corporation has authority to issue 40,000,000 shares of Common
        Stock of the par value of $1.25 per share (the "Common Stock") and
        10,000,000 shares of Preferred Stock of the par value of $.05 per share
        (the "Preferred Stock"). Upon the effectiveness of the amendments
        contained in these Articles of Amendment (the "Effective Date") each
        share of common stock of the Corporation issued at the close of business
        on the Effective Date shall be changed and split-up into two shares of
        Common Stock without change in the aggregate amount of capital
        represented by the issued shares, such two-for-one split to be
        accomplished by issuing to each holder of the Corporation's common stock
        of record at the close of business on the Effective Date a certificate
        or certificates at the rate of one additional share of Common Stock for
        each share of the common stock held of record on the stock transfer
        records of the Corporation at the close of business on the Effective
        Date.
 
          (2) The first sentence of Paragraph C. is deleted and there is
     substituted in its place the following:
 
             Of the aforesaid 10,000,000 shares of Preferred Stock, 1,999,998
        shares shall constitute a separate series of preferred shares designated
        "Preferred Stock, $.70 Cumulative Convertible Series A" (hereinafter
        called the "Series A Preferred Stock"), which shall have a stated value
        of $10.00 per share. Upon the Effective Date, in lieu of any adjustment
        of the conversion price or conversion rate applicable to the
        Corporation's Preferred Stock, $1.40 Cumulative Convertible Series A
        (the "Old Series A Preferred Stock") that would otherwise result from
        the foregoing two-
<PAGE>   10
 
        for-one stock split of the Corporation's common stock under Article III
        C. of the Restated Articles of Incorporation, each share of the Old
        Series A Preferred Stock issued at the close of business on the
        Effective Date shall be changed and split-up into two shares of Series A
        Preferred Stock without change in the aggregate amount of capital
        represented by the issued shares, such two-for-one split to be
        accomplished by issuing to each holder of Old Series A Preferred Stock
        of record at the close of business on the Effective Date a certificate
        or certificates at the rate of one additional share of Series A
        Preferred Stock for each share of Old Series A Preferred Stock held of
        record on the stock transfer records of the Corporation at the close of
        business on the Effective Date.
 
          (3) The first sentence of Subparagraph (1) of Paragraph C. is amended
     to read in its entirety as follows:
 
             The holders of the Series A Preferred Stock shall be entitled to
        receive, when and as declared by the Board of Directors out of the funds
        of the Corporation legally available therefor and in preference to the
        holders of the Common Stock of the Corporation and any other capital
        stock of the Corporation ranking junior to the Series A Preferred Stock
        as to dividends, cumulative preferential dividends per share of Series A
        Preferred Stock in cash at the rate per annum of $.70 and no more.
 
          (4) The first sentence of Subparagraph (4) of Paragraph C. is amended
     to read in its entirety as follows:
 
             In the event of any liquidation, dissolution or winding up of the
        affairs of the Corporation, after payment or provision for payment of
        the debts and other liabilities of the Corporation (including any
        liquidation preferences payable in respect of capital stock of the
        Corporation ranking senior to the Series A Preferred Stock as to
        assets), the holders of the Series A Preferred Stock shall be entitled
        to receive, out of the remaining net assets of the Corporation, $10.00
        in cash for each share of Series A Preferred Stock, plus an amount equal
        to all dividends accrued and unpaid on each such share (whether or not
        declared) up to the date fixed for distribution, before any distribution
        shall be made to the holders of the Common Stock of the Corporation or
        any other stock of the Corporation ranking junior to the Series A
        Preferred Stock as to assets.
 
          (5) The second and third sentences of Subparagraph (5) of Paragraph C.
     are amended to read in their entirety as follows:
 
        The result obtained by dividing $5.00 by the conversion rate in effect
        from time to time is herein referred to as the "conversion price."
        Whenever the conversion price is adjusted pursuant to the provisions of
        Subparagraph (d) below, the conversion rate shall be redetermined by
        dividing $5.00 by the then adjusted conversion price.
 
          (6) Wherever the phrase "$20.00 stated value" appears in Article
     IIIC., such phrase be and it hereby is amended to read "$10.00 stated
     value."
 
          (7) Wherever the term "Preferred Stock, $1.40 Cumulative Convertible
     Series A" appears in Article IIIC., such term shall be and it hereby is
     amended to read "Preferred Stock, $.70 Cumulative Convertible Series A."
 
     AND SAID APPEARERS further declared that of the outstanding shares of
capital stock of the Corporation 5,353,803 were represented at said meeting and
that 4,913,251 shares were voted for the said amendment and that 440,522 shares
were voted against the said amendment or abstained from voting thereon.
 
     AND SAID APPEARERS further declared that 712,000 shares of the Series A
Preferred Stock of the Corporation were represented at said meeting, and that
712,000 shares were voted for the said amendment and that no shares were voted
against the said amendment.
 
     APPEARERS FURTHER stated that all of the shares of the Corporation have par
value; that the Corporation is authorized to issue 50,000,000 shares, of which
40,000,000 are common shares of the par value
 
                                        2
<PAGE>   11
 
of $1.25 per share and 10,000,000 are preferred shares of the par value of $0.05
per share; that of the preferred shares, 1,999,998 shares have been designated
as the Series A Preferred Stock and 960,000 shares have been designated as the
Series B Preferred Stock; and that the Board of Directors of the Corporation has
the authority to amend the Articles to fix the preferences, limitations, and
relative rights of the preferred shares, and to establish, and fix variations
and relative rights and preferences as between, series of preferred shares, all
as more fully set out in Article III of the Articles of Incorporation.
 
     AND SAID APPEARERS having requested me, Notary, to note said amendment in
authentic form, I do by these presents receive said amendments in the form of
this public act to the end that said amendment may be promulgated and recorded
and thus be read into the Restated Articles of Incorporation of Southdown, Inc.,
as hereinabove set forth.
 
     THUS DONE AND PASSED, in my office at Houston, Harris County, State of
Texas, on the day, month and year first above written, in the presence of the
undersigned competent witnesses, who hereunto sign their names with the said
appearers and me, Notary, after a due reading of the whole.
 
                                            SOUTHDOWN, INC.
 
                                            By:  /s/ EDGAR J. MARSTON III
 
                                              ----------------------------------
                                                     Edgar J. Marston III
                                                   Executive Vice President
 
                                            By:   /s/ WENDELL E. PHILLIPS
 
                                              ----------------------------------
                                                   Wendell E. Phillips, II
                                                          Secretary
 
WITNESSES:
 
        /s/ JOANN PAVLOCK
- ------------------------------------
           JoAnn Pavlock
 
      /s/ MICHELLE RAYMOND
- ------------------------------------
          Michelle Raymond
 
                             /s/ SHAWNA CHISNELL
 
                       ----------------------------------
                                 NOTARY PUBLIC
 
                                 [Notary Seal]
 
                                        3
<PAGE>   12
 
                            ARTICLES OF AMENDMENT TO
                       RESTATED ARTICLES OF INCORPORATION
                              DATED MARCH 4, 1991
 
<TABLE>
<S>                                    <C>       <C>
ARTICLES OF AMENDMENT TO                 sec.    STATE OF TEXAS
RESTATED ARTICLES OF                     sec.    COUNTY OF HARRIS
INCORPORATION OF                         sec.    CITY OF HOUSTON
SOUTHDOWN, INC.                          sec.
</TABLE>
 
     BE IT KNOWN, That on this 4th day of March, 1991,
 
     BEFORE ME, JoAnn M. Pavlock, a Notary Public, duly commissioned and
qualified in and for the County of Harris, State of Texas, and in the presence
of the witnesses hereinafter named and undersigned:
 
                         PERSONALLY CAME AND APPEARED:
 
     CLARENCE C. COMER and WENDELL E. PHILLIPS, II, appearing herein and acting
for Southdown, Inc. (of which Corporation they are, respectively, President and
Secretary), a corporation organized and existing under the laws of the State of
Louisiana, domiciled in the Parish of Orleans, State of Louisiana, organized by
Articles of Incorporation effective April 4, 1930, which Articles, as amended,
were restated pursuant to Restated Articles of Incorporation effective September
15, 1983, who declared that pursuant to Sections 24B(6) and 33A of the Louisiana
Business Corporation Law, Article IIIB of the Restated Articles of Incorporation
of the Corporation, and resolutions of the Board of Directors of the Corporation
adopted at a special meeting of the Board of Directors of the Corporation held
on March 4, 1991, they now appear for the purpose of executing this act of
amendment and putting into authentic form the amendment so adopted by the Board
of Directors of said Corporation.
 
     AND THE SAID APPEARERS further declare that by vote of the Board of
Directors of said Corporation, it was resolved that Article III of the Restated
Articles of Incorporation of Southdown, Inc. be further amended as follows:
 
          1. There is added as a new paragraph E of Article III the following:
 
             E. Of the aforesaid 10,000,000 shares of Preferred Stock, 400,000
        shares shall constitute a separate series of preferred shares designated
        "Preferred Stock, Cumulative Junior Participating Series C" (the "Series
        C Preferred Stock"). The preferences, limitations and relative rights of
        the Series C Preferred Stock are as follows:
 
                                PREFERRED STOCK,
                    CUMULATIVE JUNIOR PARTICIPATING SERIES C
 
     1. Dividends. (A) The holders of the Series C Preferred Stock shall be
entitled to receive, when and as declared by the Board of Directors out of the
funds of the Corporation legally available therefor, subject to the prior and
superior rights of the holders of the Corporation's Preferred Stock, $.70
Cumulative Convertible Series A ("Series A Preferred Stock"), the Corporation's
Preferred Stock, $3.75 Convertible Exchangeable Series B ("Series B Preferred
Stock") and any other shares of any series of Preferred Stock ranking senior to
the shares of Series C Preferred Stock as to dividends, but in preference to the
holders of the Common Stock, par value $1.25 per share, of the Corporation (the
"Common Stock") and any other capital stock of the Corporation ranking junior to
the Series C Preferred Stock as to dividends, cumulative preferential dividends
per share of Series C Preferred Stock payable in cash on the last day of March,
June, September and December in each year (each such date being referred to
herein as a "Quarterly Dividend Payment Date"), commencing on the first
Quarterly Dividend Payment Date after the first issuance of a share or fraction
of a share of Series C Preferred Stock, in an amount per share (rounded to the
nearest cent) equal to the greater of (a) $2.00 or (b) subject to the provision
for adjustment hereinafter set forth, the Adjustment Number (as defined below)
times the aggregate per share amount of all cash dividends, and the Adjustment
Number times
<PAGE>   13
 
the aggregate per share amount (payable in kind) of all non-cash dividends or
other distributions other than a dividend or distribution payable in shares of
Common Stock or a subdivision of the outstanding shares of Common Stock (by
reclassification or otherwise), declared on the Common Stock since the
immediately preceding Quarterly Dividend Payment Date, or, with respect to the
first Quarterly Dividend Payment Date, since the first issuance of any share or
fraction of a share of Series C Preferred Stock. The "Adjustment Number" shall
initially be 100. In the event the Corporation shall at any time after March 4,
1991 (i) declare any dividend on Common Stock payable in shares of Common Stock,
(ii) subdivide the outstanding Common Stock or (iii) combine the outstanding
Common Stock into a smaller number of shares, then in each such case the
Adjustment Number in effect immediately prior to such event shall be adjusted by
multiplying such Adjustment Number by a fraction the numerator of which is the
number of shares of Common Stock outstanding immediately after such event and
the denominator of which is the number of shares of Common Stock that were
outstanding immediately prior to such event.
 
     (B) Dividends shall begin to accrue and be cumulative on outstanding shares
of Series C Preferred Stock from the Quarterly Dividend Payment Date next
preceding the date of issue of such shares of Series C Preferred Stock, unless
the date of issue of such shares is prior to the record date for the first
Quarterly Dividend Payment Date, in which case dividends on such shares shall
accrue and be cumulative from the date of issue of such shares, or unless the
date of issue is a Quarterly Dividend Payment Date or is a date after the record
date for the determination of holders of shares of Series C Preferred Stock
entitled to receive a quarterly dividend and before such Quarterly Dividend
Payment Date, in either of which events such dividends shall begin to accrue and
be cumulative from such Quarterly Dividend Payment Date.
 
     (C) Each dividend on the Series C Preferred Stock shall be paid to the
holders of record of shares of the Series C Preferred Stock as they appear on
the stock register of the Corporation on such record date, not exceeding 30 days
preceding the payment date thereof, as shall be fixed by the Board of Directors
of the Corporation. Dividends on account of arrears for any past dividend
periods may be declared and paid at any time, without reference to any regular
dividend payment date, to holders of record on such date, not exceeding 45 days
preceding the payment date thereof, as may be fixed by the Board of Directors of
the Corporation. No dividend may be declared on any other series or class of
stock ranking on a parity with the Series C Preferred Stock as to dividends in
respect of any dividend period, unless there shall also be or have been declared
on the Series C Preferred Stock like dividends for all periods in the amounts
provided therefor in paragraph 1(A) above. In the event that full cumulative
dividends on the Series C Preferred Stock have not been declared and paid or set
apart for payment, the Corporation may not declare or pay or set apart for
payment any dividends or make any other distributions on, or make any payment on
account of the purchase, redemption or retirement of, the Common Stock or any
other stock of the Corporation ranking junior to the Series C Preferred Stock as
to dividends or distributions of assets on liquidation, dissolution or winding
up of the Corporation (other than, in the case of dividends or distributions,
dividends or distributions paid in shares of Common Stock or such other junior
ranking stock), until full cumulative dividends on the Series C Preferred Stock
are declared and paid or set apart for payment. Further, the Corporation shall
not declare a dividend or distribution on the Common Stock unless it also
declares a dividend or distribution on the Series C Preferred Stock as provided
in paragraph (A) above immediately after it declares a dividend or distribution
on the Common Stock (other than a dividend or distribution payable in shares of
Common Stock); provided that, in the event no dividend or distribution shall be
been declared on the Common Stock during the period between any Quarterly
Dividend Payment Date and the next subsequent Quarterly Dividend Payment Date, a
dividend of $2.00 per share on the Series C Preferred Stock shall nevertheless
be payable on such subsequent Quarterly Dividend Payment Date.
 
     2. Redemption. (A) The Corporation, at its option, may redeem shares of
Series C Preferred Stock in whole at any time and in part from time to time, at
a redemption price equal to the Adjustment Number times the current per share
market price (as such term is hereinafter defined) of the Common Stock on the
date of the mailing of the notice of redemption, together with accrued and
unpaid dividends to the date of such redemption. The "current per share market
price" on any date shall be deemed to be the average of the closing price per
share of such Common Stock for the ten consecutive Trading Days (as such term is
hereinafter defined) immediately prior to such date; provided, however, that in
the event that the current per share market
 
                                        2
<PAGE>   14
 
price of the Common Stock is determined during a period following the
announcement of (A) a dividend or distribution on the Common Stock other than a
regular quarterly cash dividend or (B) any subdivision, combination or
reclassification of such Common Stock and the ex-dividend date for such dividend
or distribution, or the record date for such subdivision, combination or
reclassification, shall not have occurred prior to the commencement of such ten
Trading Day period, then, and in each such case, the current per share market
price shall be properly adjusted to take into account ex-dividend or
ex-distribution trading. The closing price for each day shall be the last sales
price, regular way, or, in case no such sale takes place on such day, the
average of the closing bid and asked prices, regular way, in either case as
reported in the principal consolidated transaction reporting system with respect
to securities listed or admitted to trading on the New York Stock Exchange, or,
if the Common Stock is not listed or admitted to trading on the New York Stock
Exchange, as reported in the principal transaction reporting system with respect
to securities listed on the principal national securities exchange on which the
Common Stock is listed or admitted to trading or, if the Common Stock is not
listed or admitted to trading on any national securities exchange, the last
quoted sales price or, if not so quoted, the average of the high bid and low
asked prices in the over-the-counter market, as reported by the National
Association of Securities Dealers, Inc. Automated Quotations System or such
other self-regulatory organization or registered securities information
processor (as such terms are used under the Securities Exchange Act of 1934, as
amended) that then reports information concerning the Common Stock or, if on any
such date the Common Stock is not quoted by any such entity, the average of the
closing bid and asked prices as furnished by a professional market maker making
a market in the Common Stock selected by the Board of Directors of the
Corporation. If on any such date no such market maker is making a market in the
Common Stock, the fair value of the Common Stock on such date as determined in
good faith by the Board of Directors of the Corporation shall be used. The term
"Trading Day" shall mean a day on which the principal national securities
exchange on which the Common Stock is listed or admitted to trading is open for
the transaction of business or, if the Common Stock is not listed or admitted to
trading on any national securities exchange, a business day.
 
     (B) In case of the redemption of only part of the Series C Preferred Stock
at the time outstanding, such redemption shall be made pro rata, provided,
however, that the Corporation shall not be required to effect the redemption in
any manner that results in fractional shares being outstanding (unless
immediately prior to such time fractional shares were outstanding, in which case
the Corporation shall not be required to effect the redemption in any manner
that results in fractions of shares, other than one-hundredths of shares, being
outstanding); if full cumulative dividends shall not have been paid or declared
and set apart for payment for all quarterly dividends to and including the last
Quarterly Dividend Payment Date prior to the date fixed for redemption, the
Corporation shall not:
 
          (i) call for redemption (except for redemptions in accordance with
     subparagraph 2(B)(iii) below) any shares of Series C Preferred Stock unless
     all such shares then outstanding are called for simultaneous redemption; or
 
          (ii) redeem or purchase or otherwise acquire (except for redemptions,
     purchases or acquisitions in accordance with subparagraph 2(B)(iii) below)
     for consideration shares of any stock ranking on a parity (either as to
     dividends or upon liquidation, dissolution or winding up) with Series C
     Preferred Stock, provided that the Corporation may at any time redeem,
     purchase or otherwise acquire shares of any such parity stock in exchange
     for shares of any stock of the Corporation ranking junior (both as to
     dividends and upon dissolution, liquidation or winding up) to Series C
     Preferred Stock; or
 
          (iii) redeem or purchase or otherwise acquire (except for redemptions,
     purchases or acquisitions in accordance with subparagraphs 2(B)(i) and
     2(B)(ii) above) for consideration any shares of Series C Preferred Stock,
     or any shares of stock ranking on a parity with Series C Preferred Stock,
     except in accordance with a purchase offer made in writing or by
     publication (as determined by the Board of Directors) to all holders of
     such shares of parity stock and Series C Preferred Stock upon such terms as
     the Board of Directors, after consideration of the respective annual
     dividend rates and other relative rights and preferences of the respective
     series and classes, shall determine in good faith will result in fair and
     equitable treatment among the respective series or classes.
 
                                        3
<PAGE>   15
 
     (C) Notice of any proposed redemption of Series C Preferred Stock shall be
given by the Corporation not less than 15 days nor more than 60 days prior to
the date fixed for such redemption to each holder of record of the shares to be
redeemed at his address appearing on the books of the Corporation. Notice of
redemption shall be deemed to have been given when deposited in the United
States mails, by first class mail, whether or not such notice is actually
received. If on or before the redemption date specified in such notice all funds
necessary for such redemption shall have been set aside by the Corporation,
separate and apart from its other funds, in trust for the pro rata benefit of
the holders of the shares so called for redemption, so as to be and continue to
be available therefor, then from and after the date of redemption so designated,
notwithstanding that any certificate representing shares of Series C Preferred
Stock so called for redemption shall not have been surrendered for cancellation,
the shares represented thereby shall no longer be deemed outstanding, the right
to receive dividends thereon shall cease to accrue and all rights with respect
to such shares of Series C Preferred Stock so called for redemption shall
forthwith at the close of business on such redemption date cease and terminate,
except only the right of the holders thereof to receive the redemption price of
such shares so to be redeemed plus an amount equal to accrued and unpaid
dividends (whether or not declared) up to the date fixed for redemption, but
without interest thereon.
 
     (D) The Corporation may, however, prior to the redemption date specified in
the notice of redemption, deposit in trust for the account of the holders of the
shares of Series C Preferred Stock to be redeemed, with a bank or trust company
in good standing organized under the laws of the United States of America or of
any state thereof, having its principal office located in the continental United
States, and having a capital, surplus and undivided profits aggregating at least
$50 million, designated in such notice of redemption, all funds necessary for
such redemption (including accrued and unpaid dividends up to the date fixed for
redemption), together with irrevocable written instructions authorizing such
bank or trust company, on behalf and at the expense of the Corporation, to cause
the notice of redemption to be mailed as herein provided at least 15 days but
not more than 60 days prior to the redemption date and to include in said notice
of redemption a statement that all funds necessary for such redemption have been
so deposited in trust and are immediately available, and on the redemption date,
notwithstanding that any certificate representing shares of Series C Preferred
Stock called for redemption shall not have been surrendered for cancellation,
all shares of Series C Preferred Stock with respect to which such deposit shall
have been made and which are outstanding on such redemption date shall no longer
be deemed to be outstanding and all rights with respect to such shares of Series
C Preferred Stock shall forthwith at the close of business on such redemption
date cease and terminate, except only the right of the holders thereof to
receive from such bank or trust company, at any time after the redemption date,
the redemption price of such shares so to be redeemed plus accrued and unpaid
dividends up to the date fixed for redemption.
 
     (E) If any shares of Series C Preferred Stock called for redemption are not
issued and outstanding as of the date fixed for redemption, the amount set aside
or deposited for the redemption thereof shall revert to or be paid over to the
Corporation.
 
     (F) Any shares of Series C Preferred Stock which are redeemed or otherwise
purchased or acquired by the Corporation or any subsidiary thereof shall be
cancelled. The number of shares of Series C Preferred Stock shall be reduced by
the number of shares so cancelled and such cancelled shares shall be restored to
the status of authorized but unissued shares of Preferred Stock that are
undesignated as to series. For the purposes of this paragraph, a subsidiary
means a corporation of which a majority of the capital stock having voting power
under ordinary circumstances to elect a majority of the board of directors is
owned by (a) the Corporation, (b) the Corporation and one or more of its
subsidiaries or (c) one or more of the Corporation's subsidiaries.
 
     3. Regarding Voting Rights. The holders of shares of Series C Preferred
Stock shall have the following voting rights:
 
          (A) Each share of Series C Preferred Stock shall entitle the holder
     thereof to a number of votes equal to the Adjustment Number for each share
     held and, except as otherwise provided herein or by law, the Series A
     Preferred Stock, the Series B Preferred Stock, the Series C Preferred Stock
     and the Common Stock (and any other capital stock of the Corporation
     entitled to vote) shall vote together as a single class.
 
                                        4
<PAGE>   16
 
          (B) Unless the vote of a larger percentage is required by law or the
     Restated Articles of Incorporation, the affirmative vote of the holders of
     a majority of the outstanding shares of Series C Preferred Stock shall be
     sufficient to take any action as to which a class vote of the holders of
     the Series C Preferred Stock is required by law or the Restated Articles of
     Incorporation.
 
          (C) Whenever, at any time, dividends payable on the Series C Preferred
     Stock shall be in arrears for such number of dividend payments as shall
     include not less than 540 calendar days, the holders of all Preferred Stock
     (including holders of the Series C Preferred Stock) upon which these or
     like voting rights have been conferred (without limiting the generality of
     the foregoing, not including the Series A Preferred Stock and the Series B
     Preferred Stock) and are exercisable (the "Voting Preferred Stock") with
     dividends in arrears for such number of dividend payments as shall include
     not less than 540 calendar days, shall have the exclusive right, voting
     separately as a class, irrespective of series, to elect by a majority of
     the votes cast two directors of the Corporation, (i) at the Corporation's
     next annual meeting of the shareholders, (ii) at a special meeting held in
     place thereof, (iii) at a special meeting of the holders of shares of the
     Voting Preferred Stock called by the Secretary of the Corporation upon the
     written request of the holders of record of 25% or more of the total number
     of shares of Voting Preferred Stock then outstanding, to be held within 30
     days after delivery of such request, or (iv) by written consent of the
     holders of a majority of the issued and outstanding shares of Voting
     Preferred Stock in lieu thereof, and at each meeting of shareholders
     thereafter at which directors shall be elected until such rights shall
     terminate as hereinafter provided. The Board of Directors of the
     Corporation hereby unanimously directs the Secretary of the Corporation to
     give notice of any special meeting of the shareholders of the Corporation
     required from time to time by the provisions of this paragraph, in the
     manner prescribed by the Bylaws of the Corporation. Upon the vesting of
     such voting right in the holders of the Voting Preferred Stock, the maximum
     authorized number of members of the Board of Directors shall automatically
     be increased by two and the two vacancies so created shall be filled by
     vote of the holders of the Voting Preferred Stock as hereinabove set forth.
     The right of the holders of the Voting Preferred Stock, voting separately
     as a class, to elect members of the Board of Directors of the Corporation
     as aforesaid shall continue until such time as all dividends accumulated on
     the Series C Preferred Stock shall have been paid in full, at which time
     such right shall terminate, except as by law expressly provided, subject to
     revesting in the event of each and every subsequent default of the
     character above mentioned. Upon any termination of the right of the holders
     of the Voting Preferred Stock to vote for directors as herein provided, the
     term of office of all directors then in office elected by such Voting
     Preferred Stock voting as a class shall terminate immediately. If the
     office of any director elected by the holders of the Voting Preferred Stock
     becomes vacant by reason of death, resignation, retirement,
     disqualification, removal from office, or otherwise, the remaining director
     elected by the holders of Voting Preferred Stock voting as a class may
     choose a successor who shall hold office for the unexpired term in respect
     of which such vacancy occurred. Whenever the special voting powers vested
     in the holders of the Voting Preferred Stock shall be expired, the number
     of directors shall become such number as may be provided for in the Bylaws,
     or resolution of the Board of Directors thereunder, irrespective of any
     increase made pursuant to the provisions of this paragraph 3.
 
          (D) At any time that any shares of Series C Preferred Stock are
     outstanding, the Restated Articles of Incorporation, as amended, of the
     Corporation shall not be amended in any manner which would materially alter
     or change the powers, preferences or special rights of Series C Preferred
     Stock so as to affect them adversely without the affirmative vote of the
     holders of a majority or more of the outstanding shares of Series C
     Preferred Stock, voting separately as a class.
 
     4. Priority in Event of Dissolution. (A) Upon any liquidation (voluntary or
otherwise), dissolution or winding up of the Corporation, no distribution shall
be made to the holders of shares of stock ranking junior (either as to dividends
or upon liquidation, dissolution or winding up) to the Series C Preferred Stock
unless, prior thereto, the holders of shares of Series C Preferred Stock shall
be received $100 per share, plus an amount equal to accrued and unpaid dividends
and distributions thereon, whether or not declared, to the date of such payment
(the "Series C Liquidation Preference"). Following the payment of the full
amount of the Series C Liquidation Preference, no additional distributions shall
be made to the holders of shares of Series C
                                        5
<PAGE>   17
 
Preferred Stock unless, prior thereto, the holders of shares of Common Stock
shall have received an amount per share (the "Common Adjustment") equal to the
quotient obtained by dividing (i) the Series C Liquidation Preference by (ii)
the Adjustment Number. Following the payment of the full amount of the Series C
Liquidation Preference and the Common Adjustment in respect of all outstanding
shares of Series C Preferred Stock and Common Stock, respectively, holders of
Series C Preferred Stock and holders of shares of Common Stock shall receive
their ratable and proportionate share of the remaining assets to be distributed
in the ratio of the Adjustment Number to 1 with respect to such Series C
Preferred Stock and Common Stock, on a per share basis, respectively.
 
     (B) In the event, however, that there are not sufficient assets available
to permit payment in full of the Series C Liquidation Preference and the
liquidation preferences of all other series of Preferred Stock, if any, that
rank on a parity with Series C Preferred Stock, then such remaining assets shall
be distributed ratably to the holders of such parity shares (including the
Series C Preferred Stock) in proportion to their respective liquidation
preferences.
 
     5. Consolidation, Merger, etc. In case the Corporation shall enter into any
consolidation, merger, combination or other transaction in which the shares of
Common Stock are exchanged for or changed into other stock or securities, cash
and/or any other property, then in any such case the shares of Series C
Preferred Stock shall at the same time be similarly exchanged or changed in an
amount per share equal to the Adjustment Number times the aggregate amount of
stock, securities, cash and/or any other property (payable in kind), as the case
may be, into which or for which each share of Common Stock is changed or
exchanged.
 
     6. Ranking. The Series C Preferred Stock shall rank junior to the Series A
Preferred Stock and Series B Preferred Stock as to the payment of dividends and
distribution of assets, and shall also rank junior to all other series of the
Corporation's Preferred Stock as to the payment of dividends and the
distribution of assets, unless the terms of any such series shall provide
otherwise.
 
     7. Fractional Shares. The Series C Preferred Stock may be issued in
fractions of a share that shall entitle the holder, in proportion to such
holder's fractional shares, to exercise voting rights, receive dividends,
participate in distributions and to have the benefit of all other rights of
holders of Series C Preferred Stock.
 
     8. Sinking Fund. The Series C Preferred Stock shall not be entitled to any
mandatory redemption or prepayment (except on liquidation, dissolution or
winding up of the affairs of the Corporation) or to the benefit of any sinking
fund.
 
     9. Amount. The number of shares of Series C Preferred Stock may be
increased or decreased by resolution of the Board of Directors; provided,
however, that no decrease shall reduce the number of shares of Series C
Preferred Stock to less than the number of shares then issued and outstanding
plus the number of shares issuable upon exercise of outstanding rights, options
or warrants or upon conversion of outstanding securities issued by the
Corporation.
 
     10. Definition. If the day upon which any payment is to be made or any
other action is to be taken or any event is scheduled to occur pursuant to the
terms of these Articles of Amendment is not a business day, the payment shall be
made or the other action shall be taken on the next succeeding business day. A
"business day" is defined as a day in the City of Houston, County of Harris,
Texas, that is not a legal holiday or a day on which banking institutions are
authorized or obligated by law to close.
 
     11. Notice. Except as otherwise provided herein, any notice, demand or
other communication shall be deemed given and received as of the date of
delivery in person or receipt set forth on the return receipt. The inability to
delivery because of rejection or other refusal to accept any notice, demand or
other communication shall be deemed to be receipt of such notice, demand or
other communication as of the date of such inability to deliver or rejection or
refusal to accept.
 
     12. Paragraph E of Article III is relettered as paragraph F.
 
     APPEARERS further stated that all of the shares of the Corporation have par
value; that the Corporation is authorized to issue 50,000,000 shares, of which
40,000,000 are common shares of the par value
 
                                        6
<PAGE>   18
 
of $1.25 and 10,000,000 are preferred shares of the par value of $0.05 per
share; that of the preferred shares, 1,999,998 shares have been designated as
the Series A Preferred Stock, 960,000 shares have been designated as the Series
B Preferred Stock, and 400,000 have been designated as the Series C Preferred
Stock; and that the Board of Directors of the Corporation has the authority to
amend the Articles to fix the preferences, limitations, and relative rights of
the preferred shares, and to establish, and fix variations and relative rights
and preferences as between series of preferred shares, all as more fully set out
in Article III of the Restated Articles of Incorporation.
 
     AND SAID APPEARERS having requested me, Notary, to note said amendment in
authentic form, I do by these presents receive said amendment in the form of
this public act to the end that said amendment may be promulgated and recorded
and thus be read into the Restated Articles of Incorporation of Southdown, Inc.,
as hereinabove set forth.
 
     THUS DONE AND PASSED, in my office at Houston, Harris County, State of
Texas, on the day, month and year first above written, in the presence of the
undersigned competent witnesses, who hereunto sign their names with the said
appearers and me, Notary, after a due reading of the whole.
 
                                            SOUTHDOWN, INC.
 
                                            By:    /s/ CLARENCE C. COMER
                                              ----------------------------------
                                                      Clarence C. Comer
                                                          President
 
                                            By: /s/ WENDELL E. PHILLIPS, II
                                              ----------------------------------
                                                   Wendell E. Phillips, II
                                                          Secretary
 
WITNESSES:
 
       /s/ JOANNA FLANAGAN
- ------------------------------------
          JoAnna Flanagan
 
      /s/ LINDA F. HARRELL
- ------------------------------------
          Linda F. Harrell
 
                            /s/ JOANN M. PAVLOCK
               -------------------------------------------------
                                 NOTARY PUBLIC
 
                                 [Notary Seal]
 
                                        7
<PAGE>   19
 
                            ARTICLES OF AMENDMENT TO
                       RESTATED ARTICLES OF INCORPORATION
                              DATED JUNE 25, 1998
 
<TABLE>
<S>                                <C>
ARTICLES OF AMENDMENT TO    )
RESTATED ARTICLES OF        )      STATE OF TEXAS
INCORPORATION OF            )      COUNTY OF HARRIS
SOUTHDOWN, INC.             )      CITY OF HOUSTON
</TABLE>
 
     BE IT KNOWN, That on this 25th day of June, 1998
 
     BEFORE ME, Linda F. Harrell, a Notary Public, duly commissioned and
qualified in and for the County of Harris, State of Texas, and in the presence
of the witnesses hereinafter named and undersigned:
 
                         PERSONALLY CAME AND APPEARED:
 
     CLARENCE C. COMER and PATRICK S. BULLARD, appearing herein and acting for
Southdown, Inc. (of which Corporation they are, respectively, President and
Secretary), a corporation organized and existing under the laws of the State of
Louisiana, domiciled in the Parish of Orleans, State of Louisiana, organized by
Articles of Incorporation effective April 4, 1930, which Articles, as amended,
were restated pursuant to Restated Articles of Incorporation effective September
15, 1983, and further amended as of April 10, 1987, December 2, 1987, April 23,
1988, May 23, 1988, March 4, 1991 and January 25, 1994 ("the Corporation"), who
declared that pursuant to Sections 24B(6) and 33A of the Louisiana Business
Corporation Law, Article IIIB of the Restated Articles of Incorporation of the
Corporation, resolutions of the Board of Directors of the Corporation adopted at
regular and special meetings of the Board of Directors of the Corporation held
on March 17, 1998 and March 26, 1998, and resolutions of its duly authorized
Special Committee unanimously adopted at a special meeting of such committee
held on May 5, 1998, they now appear for the purpose of executing this act of
amendment and putting into authentic form the amendment so adopted by the
Special Committee of the Board of Directors of the Corporation.
 
     AND THE SAID APPEARERS further declare that by a vote of the shareholders
of said Corporation, it was:
 
     RESOLVED, that Article III of the Restated Articles of Incorporation of
Southdown, Inc. be amended so that:
 
          1. Paragraph A. is amended to read in its entirety as follows:
 
             A. The Corporation has authority to issue 200,000,000 shares of
        Common Stock of the par value of $1.25 per share (the "Common Stock")
        and 10,000,000 shares of Preferred Stock of the par value of $.05 per
        share (the "Preferred Stock").
 
     AND SAID APPEARERS further declare that of the outstanding shares of
capital stock of the Corporation 20,816,924 were represented at said meeting and
that 17,195,420 shares were voted for the said amendment and that 1,034,005
shares were voted against the said amendment or abstained from voting thereon.
 
     APPEARERS FURTHER stated that all of the shares of the Corporation have par
value; that the Corporation is authorized to issue 210,000,000 shares, of which
200,000,000 are common shares of the par value of $1.25 per share and 10,000,000
are preferred shares of the par value of $0.05 per share; and that the Board of
Directors of the Corporation and the Special Committee thereof each has the
authority to amend the articles to fix the preferences, limitations and relative
rights of the preferred shares, and to establish, and fix variations and
relative rights and preferences as between series of preferred shares, all as
more fully set out in Article III of the Restated Articles of Incorporation.
 
     AND SAID APPEARERS having requested me, Notary, to note said amendment in
authentic form, I do by these presents receive said amendments in the form of
this public act to the end that said amendment
<PAGE>   20
 
may be promulgated and recorded and thus be read into the Restated Articles of
Incorporation of Southdown, Inc., as hereinabove set forth.
 
     THUS DONE AND PASSED, in my office at Houston, Harris County, State of
Texas, on the day, month and year first above written, in the presence of the
undersigned competent witnesses, who hereunto sign their names with the said
appearers and me, Notary, after a due reading of the whole.
 
                                            SOUTHDOWN, INC.
 
                                            By:    /s/ CLARENCE C. COMER
 
                                              ----------------------------------
                                                      Clarence C. Comer
                                                President and Chief Executive
                                                            Officer
 
                                            By:   /s/ PATRICK S. BULLARD
 
                                              ----------------------------------
                                                      Patrick S. Bullard
                                              Vice President -- General Counsel
                                                        and Secretary
 
WITNESSES:
 
      /s/ J. BRUCE TOMPKINS
- ------------------------------------
         J. Bruce Tompkins
 
      /s/ MICHELLE RAYMOND
- ------------------------------------
          Michelle Raymond
 
                            /s/ LINDA F. HARRELL
             ------------------------------------------------------
                                 NOTARY PUBLIC
 
                                 [Notary Seal]
 
                                        2
<PAGE>   21
 
                            ARTICLES OF AMENDMENT TO
                     RESTATED CERTIFICATE OF INCORPORATION
                              DATED JULY 16, 1998
 
<TABLE>
<S>                             <C>          <C>
ARTICLES OF AMENDMENT TO        )            STATE OF TEXAS
RESTATED ARTICLES OF            )            COUNTY OF HARRIS
INCORPORATION OF                )            CITY OF HOUSTON
SOUTHDOWN, INC.                 )
</TABLE>
 
     BE IT KNOWN, That on this 16th day of July, 1998,
 
     BEFORE ME, Linda F. Harrell, a Notary Public, duly commissioned and
qualified in and for the County of Harris, State of Texas, and in the presence
of the witnesses hereinafter named and undersigned:
 
                         PERSONALLY CAME AND APPEARED:
 
     PATRICK S. BULLARD and THOMAS E. DAMAN, appearing herein and acting for
Southdown, Inc. (of which corporation they are, respectively, Vice
President -- General Counsel & Secretary and Vice President -- Treasurer), a
corporation organized and existing under the laws of the State of Louisiana,
domiciled in the Parish of Orleans, State of Louisiana, organized by Articles of
Incorporation effective April 4, 1930, which Articles, as amended, were restated
pursuant to Restated Articles of Incorporation effective September 15, 1983, and
further amended as of April 10, 1987, December 2, 1987, April 23, 1988, May 23,
1988, March 4, 1991, January 25, 1994 and June 26, 1998 (the "Corporation"), who
declared that pursuant to Sections 24B(6) and 33A of the Louisiana Business
Corporation Law, Article IIIB of the Restated Articles of Incorporation of the
Corporation and resolutions of the Board of Directors of the Corporation adopted
at a special meeting of the Board of Directors of the Corporation held on March
17, 1998, they now appear for the purpose of executing this act of amendment and
putting into authentic form the amendment so adopted by the Board of Directors
of the Corporation.
 
     AND THE SAID APPEARERS further declare that by a unanimous vote of the
Board of Directors of said Corporation, it was:
 
     RESOLVED, that Article III of the Restated Articles of Incorporation of
Southdown, Inc. be amended so that:
 
          1. The first sentence of Article III, Paragraph E. is hereby deleted
     and there is substituted in its place the following:
 
             E. Of the aforesaid 10,000,000 shares of Preferred Stock, 2,000,000
        shares shall constitute a separate series of preferred shares designated
        "Preferred Stock, Cumulative Junior Participating Series C" (the "Series
        C Preferred Stock").
 
     APPEARERS further stated that all of the shares of the Corporation have par
value; that the Corporation is authorized to issue 210,000,000 shares, of which
200,000,000 are common shares of the par value of $1.25 and 10,000,000 are
preferred shares of the par value of $0.05 per share; that of the preferred
shares, 2,000,000 have been designated as the Series C Preferred Stock; and that
the Board of Directors of the Corporation has the authority to amend the
Articles to fix the preferences, limitations, and relative rights of the
preferred shares, and to establish, and fix variations and relative rights and
preferences as between, series of preferred shares, all as more fully set out in
Article III of the Articles of Incorporation.
 
     AND SAID APPEARERS having requested me, Notary, to note said amendment in
authentic form, I do by these presents receive said amendments in the form of
this public act to the end that said amendment may be promulgated and recorded
and thus be read into the Restated Articles of Incorporation of Southdown, Inc.,
as hereinabove set forth.
<PAGE>   22
 
     THUS DONE AND PASSED, in my office at Houston, Harris County, State of
Texas, on the day, month and year first above written, in the presence of the
undersigned competent witnesses, who hereunto sign their names with the said
appearers and me, Notary, after a due reading of the whole.
 
                                            SOUTHDOWN INC.
 
                                            By: /s/ PATRICK S. BULLARD
                                              ----------------------------------
                                                Patrick S. Bullard, Vice
                                                President -- General Counsel and
                                                Secretary
 
                                            By: /s/ THOMAS E. DAMAN
                                              ----------------------------------
                                                Thomas E. Daman 
                                                Vice President -- Treasurer
 
WITNESSES:
 
       /s/ MARGARET NUNEZ
- ------------------------------------
           Margaret Nunez
 
    /s/ JOHN RANDALL THOMPSON
- ------------------------------------
       John Randall Thompson
 
                            /s/ LINDA F. HARRELL
 
                       ----------------------------------
                                 NOTARY PUBLIC
 
                              [Notary Public Seal]
 
     NOTE WITH RESPECT TO EXHIBIT 3.1 TO REGISTRATION STATEMENT ON FORM S-8
 
     Articles of Amendment to Restated Articles of Incorporation of Southdown,
Inc. dated April 10, 1987 (which added paragraph C to Article III and designated
the Series A Preferred Stock), April 23, 1988 (which added paragraph D to
Article III and designated the Series B Preferred Stock), and January 25, 1994
(which added paragraph F to Article III and designated the Series D Preferred
Stock) were also filed with the Louisiana Secretary of State. All of the shares
of Preferred Stock authorized by such amendments were issued, but have now been
either converted into Common Stock or redeemed. Accordingly, none of such shares
of Preferred Stock is outstanding, and all of such shares have been returned to
the status of authorized and unissued shares of Preferred Stock, undesignated as
to series. Therefore such Articles of Amendment have been intentionally omitted
from this Exhibit 3.1.
 
                                        2

<PAGE>   1
                                                                   EXHIBIT 3.2

                           - AS AMENDED MARCH 26, 1998 -




                                     BYLAWS

                                       OF

                                 SOUTHDOWN, INC.


                                    ARTICLE I

                                  Shareholders

SECTION 1 - PLACE OF HOLDING MEETINGS

All meetings of the shareholders  shall be held at the principal business office
of the corporation in New Orleans,  Louisiana,  or at such other place as may be
specified in the notice of the meeting.

SECTION 2 - ANNUAL ELECTION OF DIRECTORS

An annual meeting of shareholders for the election of directors shall be held in
each  calendar year on such date as the board of directors may determine but not
later than 18 months  after the date of the annual  meeting  held the  preceding
year, at such time as may be specified in the notice of the meeting.

SECTION 3 - VOTING

(a)      On  demand  of any  shareholder,  the  vote  for  directors,  or on any
         questions before a meeting,  shall be by ballot. All elections shall be
         had by plurality,  and all questions decided by majority,  of the votes
         cast, except as otherwise provided by the articles or by law.

(b)      At each meeting of shareholders, a list of the shareholders entitled to
         vote,  arranged  alphabetically  and  certified by the transfer  agent,
         showing the number and class of shares held by each such shareholder on
         the record  date for the  meeting,  shall be produced on the request of
         any shareholder.

(c)      The date and time of the  opening and the closing of the polls for each
         matter  on which  the  shareholders  will  vote at any  meeting  of the
         shareholders  shall be  announced at the meeting by the chairman of the
         meeting.  The Board of Directors of the  corporation  (or any committee
         designated by it for that purpose) may, to the extent not prohibited by
         law, adopt by resolution such rules, regulations and procedures for the
         conduct of any meeting of  shareholders  as it may deem  appropriate or
         convenient. Except to the extent inconsistent


<PAGE>   2



         with such rules,  regulations and procedures as adopted by the Board of
         Directors  or any such  committee,  the chairman of any meeting has the
         right and authority to prescribe such rules, regulations and procedures
         and to do all such  acts  as,  in the  judgment  of the  chairman,  are
         appropriate or convenient  for the conduct of any meeting.  Such rules,
         regulations or procedures, whether adopted by the Board of Directors or
         any such  committee or prescribed by the chairman of any meeting,  may,
         to the extent  not  prohibited  by law,  include,  without  limitation,
         establishment of the following:  (1) an agenda or order of business for
         the meeting;  (2) rules,  regulations  and procedures  for  maintaining
         order at the meeting and the safety of those present;  (3)  limitations
         on attendance at or  participation  in the meeting to  shareholders  of
         record  of the  corporation,  their  duly  authorized  and  constituted
         proxies or such other  persons as the  chairman  of the  meeting  shall
         determine;  (4)  restrictions  on entry to the  meeting  after the time
         fixed for the  commencement  thereof;  and (5)  limitations on the time
         allotted  to  questions  or comments by  participants  at the  meeting.
         Unless, and to the extent,  determined by the Board of Directors,  by a
         duly appointed committee or by the chairman of the meeting, meetings of
         shareholders  are not required to be held in accordance  with the rules
         of parliamentary procedure.

SECTION 4 - QUORUM

Except as provided herein, any number of shareholders, together holding at least
a majority of the outstanding  shares entitled to vote thereat,  who are present
in person or  represented  by proxy at the meeting,  constitute a quorum for the
transaction of business despite the subsequent  withdrawal or refusal to vote of
any shareholder. If notice of any meeting is mailed to the shareholders entitled
to vote at the meeting,  stating the purpose or purposes of the meeting and that
the previous meeting failed for lack of a quorum, then any number  shareholders,
present  in  person  or  represented  by proxy  and  together  holding  at least
one-fourth of the  outstanding  shares  entitled to vote  thereat,  constitute a
quorum at such meeting.

SECTION 5 - ADJOURNMENT OF MEETING

If less  than a quorum  is in  attendance  at any time for  which a  meeting  is
called,  the  meeting  may  be  adjourned  by a  majority  in  interest  of  the
shareholders present or represented and entitled to vote thereat.

SECTION 6 - SPECIAL MEETING:  HOW CALLED

Special  Meetings of the  shareholders for any purpose or purposes may be called
in the manner set forth in the Restated Articles of Incorporation.


                                        2

<PAGE>   3



SECTION 7 - NOTICE OF SHAREHOLDERS' MEETINGS

Written or printed notice,  stating the place and time of any meeting, and, if a
special meeting,  the general nature of the business to be considered,  shall be
given to each shareholder  entitled to vote thereat,  at his last known address,
at least ten days before the meeting.

SECTION 8 - FORM OF PROXIES

Without limiting the manner in which a shareholder may authorize  another person
or persons to act for him as proxy, the following shall constitute a valid means
by which a shareholder may grant such authority:

(a)      A  shareholder  may  execute a writing  authorizing  another  person or
         persons to act for him or her as proxy.  Execution may be  accomplished
         by the shareholder or his or her authorized officer, director, employee
         or agent  signing  such  writing or causing his or her  signature to be
         affixed to such  writing by any  reasonable  means  including,  but not
         limited to, by facsimile signature.

(b)      Any copy, facsimile telecommunication or other reliable reproduction of
         the  writing  created  under  subsection  (a) of this  section 8 may be
         substituted  or used in place of the  original  writing for any and all
         purposes for which the original writing could be used, including filing
         with  the  secretary  of the  corporation  at or  before  the  meeting,
         provided  that  such  copy,   facsimile   telecommunication   or  other
         reproduction  shall be a complete  reproduction  of the entire original
         writing.


                                   ARTICLE II

                                    Directors

SECTION 1 - NUMBER OF DIRECTORS

Subject to the provisions of the Restated Articles of Incorporation, as amended,
the number of directors is twelve (12). 

SECTION 2 - PLACE OF HOLDING MEETINGS

Meetings of the directors,  regular or special, may be held at any place, within
or outside Louisiana, as the board may determine.




                                        3

<PAGE>   4



SECTION 3 - MEETING AFTER ANNUAL MEETING

A meeting of the Board of  Directors  shall be held  immediately  following  the
annual meeting of shareholders, and no notice of such meeting shall be necessary
to the directors,  whether or not newly elected,  in order legally to constitute
the  meeting,  provided a quorum is  present;  or they may meet at such time and
place as fixed by the consent in writing of all of the  directors,  or by notice
given by the majority of the remaining  directors.  At such  meeting,  or at any
subsequent  meeting  called  for the  purpose,  the  directors  shall  elect the
officers of the corporation.

SECTION 4 - REGULAR DIRECTORS' MEETING

Any regular meeting of the directors may be held without  notice,  if a calendar
of regular meeting dates including the date of such meeting has been established
by the  directors  at least two weeks prior to such  meeting,  at the  principal
business  office of the  corporation or at any other location  specified in such
calendar of regular  meeting dates.  Any regular meeting of the directors may be
held in the absence of  establishment of such calendar of regular meeting dates,
or at a location other than the principal  business office of the corporation or
location specified in such calendar, by the given notice as required for special
directors' meetings.  Any proposed agenda for such regular meetings shall not be
exclusive of other matters properly brought before the meeting.

SECTION 5 - SPECIAL DIRECTORS' MEETING:  HOW CALLED

Special  meetings  of the  directors  may be  called at any time by the board of
directors or by the executive committee, if one be constituted,  by the chairman
of the board of directors, or by the president, or in writing, with or without a
meeting,  by a majority  of the  directors  or of the  members of the  executive
committee.  Special  meetings  may be held at such  place or  places  within  or
outside  Louisiana  as may be  designated  by the person or persons  calling the
meeting.

SECTION 6 - NOTICE OF SPECIAL DIRECTORS' MEETINGS

Notice of the place and time of every special  meeting of the board of directors
(and of the first meeting of the newly-elected  board, if held on notice) (i) if
given by  telephone or  telegraph  shall be  delivered  to each  director at his
residence  or usual  place of  business  at least 3 days  before the date of the
meeting, and (ii) if given by a means other than telephone or telegraph shall be
sent to each  director  at his  residence  or usual place of business at least 5
days before the date of the meeting. Any proposed agenda or statement of purpose
or purposes for a special  meeting of directors  shall not be exclusive of other
matters properly brought before the meeting.

SECTION 7 - QUORUM

At all meetings of the board, a majority of the directors in office constitute a
quorum  for the  transaction  of  business,  and the  act of a  majority  of the
directors  present at any meeting at which a quorum is present  shall be the act
of the Board of Directors, unless the concurrence of a greater

                                        4

<PAGE>   5



proportion is required for such action by law, the articles of the bylaws.  If a
quorum is not present at any meeting of directors, the directors present thereat
may  adjourn  the  meeting  from  time  to  time,   without  notice  other  than
announcement at the meeting,  until a quorum is present. If a quorum be present,
the  directors  present  may  continue  to act by vote of a majority of a quorum
until adjournment, notwithstanding the subsequent withdrawal of enough directors
to leave less than a quorum or the refusal of any directors present to vote.

SECTION 8 - REMUNERATION TO DIRECTORS

Directors,  as such, shall not receive any stated salary for their services, but
by resolution  of the Board,  expenses of  attendance,  if any, and except as to
salaried  officers or employees of the corporation or an affiliated  company,  a
fixed fee for the performance of their duties as directors, as may be determined
from time to time by resolution of the Board,  may be allowed to directors,  but
this Section does not preclude any director from serving the  corporation in any
other capacity and receiving compensation therefor.

SECTION 9 - POWERS OF DIRECTORS

The board of directors has the  management  of the business of the  corporation,
and subject to any  restrictions  imposed by law, the articles or these  bylaws,
may  exercise  all the  powers of the  corporation.  Without  prejudice  to such
general powers, the directors have the following specific powers:

(a) From time to time,  to devolve the powers and duties of any officer upon any
other person for the time being.

(b) To confer upon any officer the power to appoint, remove and suspend, and fix
and change the compensation of, subordinated officers, agents and factors.

(c) To  determine  who shall be entitled to vote,  or to assign and transfer any
shares of stock,  bonds,  debentures or other  securities of other  corporations
held by this corporation.

(d) To  delegate  any of the  powers of the  board to any  standing  or  special
committee  or to any  officer or agent (with  power to  sub-delegate)  upon such
terms as they deem fit.

SECTION 10 - RESIGNATIONS

The  resignation  of a  director  shall take  effect on  receipt  thereof by the
president or secretary,  or on any later,  date, not more than thirty days after
such receipt, specified therein.





                                        5

<PAGE>   6



SECTION 11 - TERM OF OFFICE

Each director of the  corporation  shall hold office for the full term of office
to whom he shall  have been  elected  and until his  successor  shall  have been
elected and shall qualify, or until his death, resignation or removal. The Board
of  Directors  may  remove a  director  and  declare  vacant  the office of such
director who:

(a) has been interdicted or adjudicated an incompetent,

(b) has become  incapacitated by illness or other infirmity so that, in the sole
opinion  of the Board of  Directors,  he is unable to  perform  his duties for a
period of six months or longer, or

(c) has  ceased  at any time to have the  qualifications  required  by law,  the
Restated Articles of Incorporation or these Bylaws.

The  remaining  directors  may fill any vacancy on the Board of Directors for an
unexpired  term  (including  any  vacancy  resulting  from  an  increase  in the
authorized number of directors, or from the failure of the shareholders to elect
the full number of authorized directors).

SECTION 12 - PARTICIPATION IN MEETINGS

Directors may participate in and be present at any meeting of the board by means
of  conference  telephone  or similar  communications  equipment  if all persons
participating in such meeting can hear and communicate with each other.

SECTION 13 - CHAIRMAN OF THE BOARD

The board of  directors  shall  elect one of its  members to be  chairman of the
board,  to serve in such capacity at the pleasure of the board.  In his capacity
as chairman  of the board,  he shall not be an officer of the  corporation.  The
chairman of the board shall  preside at meetings of the board of  directors  and
shareholders  and perform such other duties as from time to time may be assigned
to him by the board.

SECTION 14 - VICE CHAIRMAN OF THE BOARD

The board of directors  may elect one of its members to be vice  chairman of the
board to serve in such capacity at the pleasure of the board. In his capacity as
vice chairman of the board,  he shall not be an officer of the  corporation.  In
the absence of the chairman of the board,  the vice  chairman of the board shall
preside at meetings of the board of directors and  shareholders and perform such
other duties as from time to time may be assigned to him by the board.



                                        6

<PAGE>   7



SECTION 15 - QUALIFICATIONS FOR OFFICE

     (a) No person shall be eligible for  election or  reelection  as a director
after having  attained the age of seventy  prior to or on the day of election or
reelection.  A director who attains the age of seventy during his or her term of
office shall be eligible to serve only until the annual meeting of  shareholders
of the corporation next following such director's  seventieth birthday, at which
meeting  the  shareholders  of  the  corporation  shall  elect  such  director's
successor in accordance with Article I of these bylaws.

     (b) To be eligible for nomination or election or to continue to hold office
as a director,  a person must during each immediately  preceding 12 month period
during his term of office have  attended at least  two-thirds  of the  aggregate
number of meetings of the Board of Directors  and  Committees  of which he was a
member,  unless the  failure to attend  resulted  from  illness or other  reason
determined by the Board of Directors to excuse the failure to attend. A director
who ceases to meet this attendance  qualification shall continue in office until
the expiration of his then current term or unless his office is declared  vacant
by the Board of Directors under the preceding Section 11.



                                 ARTICLE III

                                 Committees

SECTION 1 - EXECUTIVE COMMITTEE

The board may appoint an executive  committee,  which,  when the board is not in
session,  to the full  extent  of the  powers of the  board  shall  have and may
exercise the powers of the board in the  management  of the business and affairs
of the  corporation  and may have power to authorize the seal of the corporation
to be affixed to documents, provided that the executive committee shall not have
the power to make or alter bylaws,  fill vacancies on the board or the executive
committee, or change the membership of the executive committee.

SECTION 2 - MINUTES OF MEETING OF COMMITTEES

Any  committees  designated  by the board  shall keep  regular  minutes of their
proceedings,  and shall  report  the same to the  board  when  required,  but no
approval  by the board of any  action  properly  taken by a  committee  shall be
required.

SECTION 3 - PROCEDURE

If the Board fails to designate the chairman of a committee, the Chairman of the
Board, if a member,  shall be Chairman.  Each committee shall meet at such times
as it shall determine, and at any time

                                        7

<PAGE>   8



on call of the chairman. A majority of a committee constitutes a quorum, and the
committee  may take action by vote of a majority  of the members  present at any
meeting at which there is a quorum. The Board has power to change the members of
any committee at any time, to fill vacancies,  and to discharge any committee at
any time.

SECTION 4 - PARTICIPATION IN MEETINGS

Members of a committee may  participate  in and be present at any meeting of the
committee by means of conference telephone or similar  communications  equipment
if all person  participating  in such meeting can hear and communicate with each
other.


                                   ARTICLE IV

                                    Officers

SECTION 1 - TITLES

The  officers  of  the   corporation   shall  be  a   president,   one  or  more
vice-presidents,  a treasurer, a secretary and such other officers,  including a
chief executive officer and chief operating officer,  as may, from time to time,
be elected or  appointed by the board or  appointed  by the  president.  Any two
offices may be combined in the same person, provided that no person holding more
than one office may sign, in more than one capacity,  any  certificate  or other
instrument  required by law to be signed by two  officers.  No officer need be a
director.

SECTION 2 - PRESIDENT

The president shall be the chief executive  officer of the corporation.  Subject
to the direction of the board of directors, he shall have the responsibility for
the  management and control of the business and affairs of the  corporation;  he
shall see that all orders and  resolutions  of the board are carried into effect
and direct the other officers in the  performance of their duties;  and he shall
perform all duties and have all powers that are commonly  incident to the office
of chief executive or that are assigned to him by the board of directors. In the
absence of the  chairman  of the board and the vice  chairman  of the board,  he
shall preside at shareholders' meetings and at directors' meetings.

SECTION 3 - VICE PRESIDENTS

Each vice president  shall have such powers,  and shall perform such duties,  as
shall be assigned to him by the directors,  by the chairman of the board,  or by
the president,  and, in the order determined by the board, shall, in the absence
or disability of the chairman and  president,  perform their duties and exercise
their powers.



                                        8

<PAGE>   9



SECTION 4 - TREASURER

The treasurer has custody of all funds,  securities,  evidences of  indebtedness
and other valuable  documents of the corporation.  He shall receive and give, or
cause to be given, receipts and acquittances of moneys paid in on account of the
corporation,  and  shall  pay out of the  funds on hand  all  just  debts of the
corporation  of  whatever  nature,  when  due.  He shall  enter,  or cause to be
entered,  in books of the  corporation  to be kept  for that  purpose,  full and
accurate  accounts  of all  moneys  received  and  paid  out on  account  of the
corporation,  and, whenever required by the president or the directors, he shall
render a statement of his accounts. He shall keep or cause to be kept such books
as  will  show  a true  record  of  the  expenses,  gains,  losses,  assets  and
liabilities  of the  corporation;  and he shall  perform all of the other duties
incident to the office of treasurer. If required by the board, he shall give the
corporation a bond for the faithful  discharge of his duties and for restoration
to the  corporation,  upon  termination  of his tenure,  of all  property of the
corporation under his control.

SECTION 5 - SECRETARY

The  secretary  shall  give,  or cause to be given,  notice of all  meetings  of
shareholders, directors and committees, and all other notices required by law or
by these bylaws,  and in case of his absence or refusal or neglect so to do, any
such notice may be given by the shareholders or directors upon whose request the
meeting  is called as  provided  in these  bylaws.  He shall  record  all of the
proceedings  of the  meetings  of the  shareholders,  of the  directors,  and of
committees in a book to be kept for that purpose. Except as otherwise determined
by the directors,  he has charge of the original stock books, transfer books and
stock ledgers, and shall act as transfer agent in respect of the stock and other
securities  issued  by the  corporation.  He has  custody  of  the  seal  of the
corporation,  and shall affix it to all  instruments  requiring it; and he shall
perform  such  other  duties as may be  assigned  to him by the  directors,  the
chairman of the board of directors, or the president.

SECTION 6 - ASSISTANTS

Assistant secretaries or treasurers shall have such duties as may be assigned to
them by the directors, by the chairman of the board, or by the president, and as
may be delegated to them by the secretary and treasurer respectively.


                                    ARTICLE V

                                  Capital Stock

SECTION 1 - CERTIFICATES OF STOCK

Certificates of Stock,  numbered and with the seal of the corporation affixed or
imprinted, signed by the Chairman of the Board of Directors, or the President or
Vice  President,  and the  Treasurer  or  Secretary,  shall  be  issued  to each
shareholder, certifying the number of shares owned by him in the

                                        9

<PAGE>   10



corporation.  Where such  certificate is  countersigned  (1) by a transfer agent
other than the corporation or its employee, or (2) by a registrar other than the
corporation or its employee,  any other  signature on the  certificate  may be a
facsimile.

SECTION 2 - LOST CERTIFICATES

A new certificate of stock may be issued in place of any certificate theretofore
issued by the  corporation,  alleged to have been  lost,  stolen,  mutilated  or
destroyed or mailed and not received,  and the directors may in their discretion
require the owner of the replaced  certificate  to give the  corporation a bond,
unlimited as to stated amount,  to indemnify the  corporation  against any claim
which may be made against it on account of the replacement of the certificate or
any payment made or other action taken in respect thereof.

SECTION 3 - TRANSFER OF SHARES

Shares of stock of the corporation are  transferrable  only on its books, by the
holders  thereof  in  person  or by their  duly  authorized  attorneys  or legal
representatives,   and  upon  such  transfer,   the  old  certificate  shall  be
surrendered to the person in charge of the stock transfer records,  by whom they
shall be cancelled,  and new  certificates  shall thereupon be issued.  A record
shall be made of each  transfer,  and whenever a transfer is made for collateral
security,  and not  absolutely,  it shall be so  expressed  in the  entry of the
transfer.  The board may make regulations concerning the transfer of shares, and
may in their  discretion  authorize  the  transfer  of shares  from the names of
deceased  persons  whose  estates  are not  administered,  upon  receipt of such
indemnity as they may require.

SECTION 4 - RECORD DATES

The board may fix a record date for  determining  shareholders of record for any
purpose,  such date to be not more than sixty days and, if fixed for the purpose
of determining  shareholders entitled to notice of and to vote at a meeting, not
less than ten days, prior to the date of the action for which the date is fixed.

SECTION 5 - TRANSFER AGENTS, REGISTRARS

The board may appoint and remove one or more transfer  agents and registrars for
any stock.  If such  appointments  are made,  the  transfer  agents shall effect
original  issuances of stock  certificate  and  transfers of shares,  record and
advise  the  corporation  and one  another  of  such  issuances  and  transfers,
countersign  and deliver stock  certificates,  and keep the stock,  transfer and
other  pertinent  records;  and the  registrars  shall  prevent  over-issues  by
registering and countersigning  all stock certificates  issued. A transfer agent
and registrar may be identical.





                                       10

<PAGE>   11



                                   ARTICLE VI

                            Miscellaneous Provisions

SECTION 1 - CORPORATION SEAL

The Corporate seal is circular in form, and contains the name of the corporation
and the  words  "SEAL,  LOUISIANA".  The seal may be used by  causing  it,  or a
facsimile thereof, to be impressed or affixed or otherwise reproduced.

SECTION 2 - CHECKS, DRAFTS, NOTES

All checks,  drafts,  other orders for the payment of money,  and notes or other
evidences  of  indebtedness,  issued  in the name of the  corporation,  shall be
signed by such officer or officers,  agent or agents of the  corporation  and in
such manner as shall, from time to time, be determined by the board.

SECTION 3 - FISCAL YEAR

The fiscal year of the corporation begins on January 1.

SECTION 4 - NOTICE

Whenever any notice is required by these bylaws to be given,  personal notice is
not meant  unless  expressly  so stated;  any notice is  sufficient  if given by
depositing  the  same  in a  mail  receptacle  in a  sealed  post-paid  envelope
addressed to the person entitled thereto at his last known address as it appears
on the records of the corporation;  and such notice is deemed to have been given
on the day of such mailing.

SECTION 5 - WAIVER OF NOTICE

Whenever  any  notice  of  the  time,   place  or  purpose  of  any  meeting  of
shareholders,  directors  or committee is required by law, the articles or these
bylaws, a waiver thereof in writing, signed by the person or persons entitled to
such  notice  and filed  with the  records  of the  meeting  before or after the
holding thereof,  or actual  attendance at the meeting of shareholders in person
or by proxy or at the meeting of directors or committee in person, is equivalent
to the giving of such notice except as otherwise provided by law.

SECTION 6 - INDEMNIFICATION OF OFFICERS, DIRECTORS, EMPLOYEES, AND AGENTS

(a)      The corporation  shall indemnify any person who was or is a party or is
         threatened  to be  made a party  to any  action,  suit  or  proceeding,
         whether civil, criminal, administrative or investigative, including any
         action by or in the right of the corporation by reason of the fact

                                       11

<PAGE>   12



         that  he is or  was a  director,  officer,  employee  or  agent  of the
         corporation,  or is or was serving at the request of the corporation as
         a director,  officer, employee or agent of another business, foreign or
         nonprofit corporation,  partnership, joint venture or other enterprise,
         against  expenses,  including  attorneys'  fees,  judgments,  fines and
         amounts paid in settlement  actually and reasonably  incurred by him in
         connection  with such action,  suit or  proceeding  if he acted in good
         faith and in a manner he reasonably believed to be in or not opposed to
         the best interest of the corporation,  and with respect to any criminal
         action or  proceeding,  has no reasonable  cause to believe his conduct
         was  unlawful.  However,  in case of  actions by or in the right of the
         corporation,  the  indemnity  shall be limited to  expenses,  including
         attorneys'  fees and amounts paid in settlement not  exceeding,  in the
         judgment of the board of directors, the estimated expense of litigating
         the  action  to  conclusion,   actually  and  reasonably   incurred  in
         connection  with  the  defense  or  settlement  of such  action  and no
         indemnification  shall be made in respect of any claim, issue or matter
         as to  which  such  person  shall  have  been  adjudged  by a court  of
         competent  jurisdiction,  after exhaustion of all appeals therefrom, to
         be liable for willful or intentional  misconduct in the  performance of
         his duty to the  corporation  unless  and only to the  extent  that the
         court shall determine upon application  that,  despite the adjudication
         of liability  but in view of all the  circumstances  of the case, he is
         fairly and reasonably entitled to indemnity for such expenses which the
         court  shall  deem  proper.  The  termination  of any  action,  suit or
         proceeding by judgement, order, settlement,  conviction, or upon a plea
         of nolo  contendere or its equivalent,  shall not, or itself,  create a
         presumption  that the  person did not act in good faith and in a manner
         which  he  reasonably  believed  to be in or not  opposed  to the  best
         interests of the corporation,  and, with respect to any criminal action
         or  proceeding,  had  reasonable  cause to believe that his conduct was
         unlawful.

(b)      In any event, a director, officer, employee or agent of the corporation
         who has been  successful  on the merits or  otherwise in defense of any
         such action,  suit or proceeding,  or in defense of any claim, issue or
         matter  therein,  shall  be  indemnified  against  expenses  (including
         attorneys' fees) actually and reasonably  incurred by him in connection
         therewith.

(c)      Any  indemnification  under  subsection  (a) of  this  Section,  unless
         ordered  by the  Court  shall  be  made  by  the  corporation  only  as
         authorized in a specific case upon a determination  that the applicable
         standard of conduct has been met. Such determination  shall be made (1)
         by the board of directors by a majority vote of a quorum  consisting of
         directors who were not parties to such action,  suit or proceeding,  or
         (2) if such a quorum is not  obtainable  and the board of  directors so
         directs, by independent legal counsel or (3) by the shareholders.

(d)      Expenses  incurred in defending such an action,  suit or proceeding may
         be paid by the corporation in advance of the final disposition  thereof
         if  authorized  by the board of  directors,  without  regard to whether
         participating  members  thereof are parties to such  action,  suit,  or
         proceeding,  upon  receipt  of an  undertaking  by or on  behalf of the
         director,  officer,  employee or agent to repay such amount if it shall
         ultimately be determined  that he is not entitled to be  indemnified by
         the corporation as authorized in this Section.

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<PAGE>   13



(e)  The  indemnification  and  advancement  of expenses  provided by or granted
     pursuant  to the  other  subsections  of this  Section  shall not be deemed
     exclusive of any other rights to which the person  indemnified or obtaining
     advancement of expenses is entitled under any agreement,  authorization  of
     shareholders or directors, regardless of whether directors authorizing such
     indemnification are beneficiaries thereof, or otherwise,  both as to action
     in his official capacity and as to action in another capacity while holding
     such  office,  and shall  continue  as to a person  who has  ceased to be a
     director,  officer, employee or agent and shall inure to the benefit of his
     heirs and legal  representative;  however,  no such  other  indemnification
     measure shall permit  indemnification of any person for the results of such
     person's willful or intentional misconduct.

(f)  The corporation shall have power to procure or maintain  insurance or other
     similar  arrangement  on behalf  of any  person  who is or was a  director,
     officer, employee or agent of the corporation,  or is or was serving at the
     request of the  corporation  as a director,  officer,  employee or agent of
     another  business,  nonprofit or foreign  corporation,  partnership,  joint
     venture or other  enterprise  against  any  liability  asserted  against or
     incurred by him in any such capacity, or arising out of his status as such,
     whether  or not the  corporation  would  have the  power to  indemnify  him
     against  such  liability  under the  provisions  of this  Section.  Without
     limiting the power of the corporation to procure or maintain any other kind
     of insurance or similar  arrangement,  the  corporation  may create a trust
     fund or other form of self-insurance arrangement for the benefit of persons
     indemnified by the  corporation  and may procure or maintain such insurance
     with any insurer deemed appropriate by the board of directors regardless of
     whether all or part of the stock or other  securities  thereof are owned in
     whole or part by the  corporation.  In the  absence  of actual  fraud,  the
     judgment of the board of directors as to the terms and  conditions  of such
     insurance or self-insurance  arrangement and the identity of the insurer or
     other  person  participating  in  a  self-insurance  arrangement  shall  be
     conclusive,  and such  arrangements  for insurance  shall not be subject to
     voidability and shall not subject the directors  approving such arrangement
     to liability, on any ground,  regardless of whether directors participating
     in approving such insurance  arrangements  shall be beneficiaries  thereof.
     The  provisions  of the Insurance  Code (Title 22 of the Revised  Statutes)
     will not apply to any  wholly-owned  subsidiary of this  corporation  if it
     issues  contracts of insurance  only as  permitted by this  subsection  for
     coverage of a person who is or was a director,  officer, employee, or agent
     of  this  corporation,  or who is or was  serving  at the  request  of this
     corporation as a director, officer, employee, or agent of another business,
     nonprofit or foreign  corporation,  partnership,  joint  venture,  or other
     enterprise,  which  contracts of insurance  for such  directors,  officers,
     employees,  or agents may be issued by such wholly-owned subsidiary without
     compliance with the provisions of the Insurance Code.

SECTION 7 - REDEMPTION OF CONTROL SHARES

In accordance with Section 140.1 of the Louisiana Business  Corporation Law, the
Company  may  redeem  any or all  control  shares  acquired  in a control  share
acquisition with respect to which either:

                                       13

<PAGE>   14


         (a) no acquiring  person  statement  has been filed with the Company in
         accordance with Section 137 of the Louisiana Business  Corporation Law;
         or

         (b) the  control  shares are not  accorded  full  voting  rights by the
         shareholders of the Company as provided in Section 140 of the Louisiana
         Business Corporation Law.

A redemption  pursuant to subparagraph (a) hereof may be made at any time during
the period ending sixty (60) days after the last  acquisition  of control shares
by an acquiring person. A redemption  pursuant to subparagraph (b) hereof may be
made at any time during the period  ending two (2) years  after the  shareholder
vote with respect to the voting rights of such control  shares.  Any  redemption
pursuant to this Paragraph shall be made at the fair value of the control shares
and pursuant to such  procedures as may be adopted by resolution of the Board of
Directors of the Company.


                                   ARTICLE VII

                                   Amendments

Except as otherwise  provided in the  Restated  Articles of  Incorporation,  the
shareholders  or the  directors,  by  affirmative  vote of a  majority  of those
present or  represented,  may at any meeting,  amend or alter any of the bylaws;
subject,  however,  to the right of the  shareholders  to  change or repeal  any
bylaws made or amended by the directors.


                                      14
                                      


<PAGE>   1
 
                                                                       EXHIBIT 5
 
                 [LETTERHEAD OF BRACEWELL & PATTERSON, L.L.P.]
 
                                 July 17, 1998
 
Southdown, Inc.
1200 Smith Street, Suite 2400
Houston, Texas 77002-4486
 
Ladies and Gentlemen:
 
     We have acted as counsel to Southdown, Inc., a Louisiana corporation (the
"Company"), in connection with the Registration Statement on Form S-8 filed by
the Company (the "Registration Statement") under the Securities Act of 1933, as
amended (the "Securities Act"), with respect to (i) 3,252,895 shares (the
"Shares") of the Company's Common Stock, $1.25 par value per share (together
with the associated preferred stock purchase rights being collectively referred
to as the "Common Stock") issuable upon the exercise of stock options granted
under the Southdown, Inc. 1989 Stock Option Plan (the "Southdown Plan"), and
(ii) 521,752 additional shares of Common Stock (the "Medusa Option Shares")
issuable upon the exercise of stock options granted under the Medusa Corporation
1991 Long-Term Incentive Plan (the "Medusa Plan") that was assumed by the
Company in connection with the merger on June 30, 1998 of Medusa Corporation
with a wholly-owned subsidiary of the Company pursuant to an Agreement and Plan
of Merger dated as of March 17, 1998 among Medusa Corporation, the Company and
Bedrock Merger Corp. (the "Merger Agreement").
 
     We have examined copies of (i) the Restated Articles of Incorporation of
the Company, as amended, (ii) the Bylaws of the Company, as amended, (iii) the
Plan, (iv) certain resolutions of the Board of Directors and shareholders of the
Company, (v) the Registration Statement, (vi) the Merger Agreement, (vii) the
Medusa Plan and (viii) such other documents and records as we have deemed
necessary and relevant for purposes hereof. In addition, we have relied on
representations of officers of the Company and certificates of public officials
as to certain matters of fact relating to this opinion and have made such
investigations of law as we have deemed necessary and relevant. We have assumed
the genuineness of all signatures, the authenticity of all documents and records
and submitted to us as originals, the conformity to authentic original documents
and records of all documents and records submitted to us as copies, and the
truthfulness of all statements of fact contained therein.
 
     Based on the foregoing, and subject to the limitations and assumptions set
forth herein, and having due regard for such legal considerations as we deem
relevant, we are of the opinion that:
 
          1. The Company is duly incorporated, validly existing and in good
     standing under the laws of the State of Louisiana.
 
          2. The Shares have been duly authorized and, when issued in accordance
     with the provisions and conditions of the Plan, will be validly issued,
     fully paid and nonassessable.
 
          3. The Medusa Option Shares have been duly authorized and, when issued
     in accordance with the provisions and conditions of the Medusa Plan, will
     be validly issued, fully paid and nonassessable.
 
     The foregoing opinion is based on and is limited to the law of the State of
Texas, the law of the State of Louisiana and the relevant law of the United
States of America, and we render no opinion with respect to the law of any other
jurisdiction. Insofar as the law of the State of Louisiana is applicable to the
matters discussed herein, we have relied exclusively upon the opinion of Correro
Fishman Haygood Phelps Weiss Walmsley & Casteix, LLP, a copy of which is annexed
hereto, and our opinion is subject to the qualifications, limitations and
assumptions set forth therein.
<PAGE>   2
Southdown, Inc.
July 16, 1998
Page 2
 
     We hereby consent to the filing of this opinion as Exhibit 5 to the
Registration Statement. In giving this consent, we do not hereby admit that we
are in the category of persons whose consent is required pursuant to Section 7
of the Securities Act.
 
                                            Very truly yours,
 
                                            /s/ BRACEWELL & PATTERSON, L.L.P.
                                            ------------------------------------
                                            Bracewell & Patterson, L.L.P.
<PAGE>   3
 
                            [CORRERO FISHMAN HAYGOOD
 
              PHELPS WEISS WALMSLEY & CASTEIX, L.L.P. LETTERHEAD]
 
                                 July 17, 1998
 
Bracewell & Patterson, L.L.P.
711 Louisiana St., Suite 2900
Houston, TX 77003
 
Ladies and Gentlemen:
 
     We have acted as special Louisiana counsel to Southdown, Inc., a Louisiana
corporation (the "Company"), in connection with the Registration Statement on
Form S-8 filed by the Company (the "Registration Statement") under the
Securities Act of 1933, as amended (the "Securities Act"), with respect to (i)
3,252,895 shares (the "Shares") of the Company's Common Stock, $1.25 par value
per share (together with the associated preferred stock purchase rights being
collectively referred to as the "Common Stock") issuable under the Southdown,
Inc. 1989 Stock Option Plan (the "Southdown Plan"), and (ii) 521,752 additional
shares of Common Stock (the "Medusa Option Shares") issuable upon the exercise
of stock options granted under the Medusa Corporation 1991 Long-Term Incentive
Plan (the "Medusa Plan") that was assumed by the Company in connection with the
merger on June 30, 1998 of Medusa Corporation with a wholly-owned subsidiary of
the Company pursuant to an Agreement and Plan of Merger dated as of March 17,
1998 among Medusa Corporation, the Company and Bedrock Merger Corp. (the "Merger
Agreement").
 
     We have examined copies of (i) the Restated Articles of Incorporation of
the Company, as amended, (ii) the Bylaws of the Company, as amended, (iii) the
Plan, (iv) certain resolutions of the Board of Directors and shareholders of the
Company, (v) the Registration Statement, (vi) the Merger Agreement, (vii) the
Medusa Plan and (viii) such other documents and records as we have deemed
necessary and relevant for purposes hereof. In addition, we have relied on
representations of officers of the Company and certificates of public officials
as to certain matters of fact relating to this opinion and have made such
investigations of law as we have deemed necessary and relevant. We have assumed
the genuineness of all signatures, the authenticity of all documents and records
and submitted to us as originals, the conformity to authentic original documents
and records of all documents and records submitted to us as copies, and the
truthfulness of all statements of fact contained therein.
 
     Based on the foregoing, and subject to the limitations and assumptions set
forth herein, and having due regard for such legal considerations as we deem
relevant, we are of the opinion that:
 
     1. The Company is duly incorporated, validly existing and in good standing
        under the laws of the State of Louisiana;
 
     2. The Shares have been duly authorized and, when issued in accordance with
        the provisions and conditions of the Plan, will be validly issued, fully
        paid and nonassessable.
 
     3. The Medusa Option Shares have been duly authorized and, when issued in
        accordance with the provisions and conditions of the Medusa Plan, will
        be validly issued, fully paid and nonassessable.
 
     The foregoing opinion is based on and is limited to the law of the State of
Louisiana, and we render no opinion with respect to the law of any other
jurisdiction.
<PAGE>   4
 
     We hereby consent to the filing of this opinion as Exhibit 5 to the
Registration Statement. In giving this consent, we do not hereby admit that we
are in the category of persons whose consent is required pursuant to Section 7
of the Securities Act.
 
                                        Very truly yours,
 
                                        Correro, Fishman, Haygood,
                                          Phelps, Weiss, Walmsley & Casteix,
                                        L.L.P.
 
                                        By:   /s/ ROBERT M. WALMSLEY, JR.
                                           -------------------------------------
                                           Robert M. Walmsley, Jr.

<PAGE>   1
 
                                                                      EXHIBIT 15
 
July 17, 1998
 
Southdown, Inc.
1200 Smith, Suite 2400
Houston, Texas 77002
 
We have made a review, in accordance with standards established by the American
Institute of Certified Public Accountants, of the unaudited interim financial
information of Southdown, Inc. and subsidiary companies for the periods ended
March 31, 1998 and 1997, as indicated in our report dated April 16, 1998;
because we did not perform an audit, we expressed no opinion on that
information.
 
We are aware that our report referred to above, which was included in your
Quarterly Report on Form 10-Q for the quarter ended March 31, 1998 is being used
in this Registration Statement.
 
We also are aware that the aforementioned report, pursuant to Rule 436(c) under
the Securities Act of 1933, are not considered a part of the Registration
Statement prepared or certified by an accountant or a report prepared or
certified by an accountant within the meaning of Sections 7 and 11 of that Act.
 
DELOITTE & TOUCHE LLP
 
Houston, Texas

<PAGE>   1
 
                                                                    EXHIBIT 23.2
 
                         INDEPENDENT AUDITORS' CONSENT
 
We consent to the incorporation by reference in this Registration Statement of
Southdown, Inc. on Form S-8 of our report dated January 27, 1998, appearing in
the Annual Report on Form 10-K of Southdown, Inc. for the year ended December
31, 1997.
 
DELOITTE & TOUCHE LLP
 
Houston, Texas
July 17, 1998


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