VALERO ENERGY CORP/TX
4, 1998-07-09
PETROLEUM REFINING
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UNITED STATES SECURITIES AND EXCHANGE COMMISSION
WASHINGTON, D.C. 20549
FORM 4
STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP
( ) Check this box if no longer subject to Section 16.
Form 4 or Form 5 obligations may continue. See Instructions 1(b).
1. Name and Address of Reporting Person
   Edwards, S. Eugene
   7990 West IH 10
   San Antonio, TX  78230
   USA
2. Issuer Name and Ticker or Trading Symbol
   Valero Energy Corporation
   VLO
3. IRS or Social Security Number of Reporting Person (Voluntary)
   ###-##-####
4. Statement for Month/Year
   06/30/98
5. If Amendment, Date of Original (Month/Year)
   
6. Relationship of Reporting Person(s) to Issuer (Check all applicable)
   ( ) Director ( ) 10% Owner (X) Officer (give title below) ( ) Other
   (specify below)
   Vice President
7. Individual or Joint/Group Filing (Check Applicable Line)
   (X) Form filed by One Reporting Person
   ( ) Form filed by More than One Reporting Person
<TABLE>
<CAPTION>
___________________________________________________________________________________________________________________________________
 Table I -- Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned                                                 |
___________________________________________________________________________________________________________________________________|
1. Title of Security       |2.    |3.    |4.Securities Acquired (A)         |5.Amount of        |6.Dir |7.Nature of Indirect       |
                           | Transaction |  or Disposed of (D)              |  Securities       |ect   |  Beneficial Ownership     |
                           |      |      |                                  |  Beneficially     |(D)or |                           |
                           |      |    | |                  | A/|           |  Owned at         |Indir |                           |
                           | Date |Code|V|    Amount        | D |    Price  |  End of Month     |ect(I)|                           |
___________________________________________________________________________________________________________________________________|
<S>                        <C>    <C>  <C><C>               <C> <C>         <C>                 <C>    <C>
Common Stock ($.01 par valu|06/05/|S   | |2,450             |D  |$34.1875   |                   |      |                           |
e)                         |98    |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock ($.01 par valu|06/30/|S   | |1,107             |D  |$32.8125   |6,872              |D     |                           |
e)                         |98    |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
Common Stock ($.01 par valu|      |    | |                  |   |           |9,927.787          |I(1)  |401(k) and other plans     |
e)                         |      |    | |                  |   |           |                   |      |                           |
- -----------------------------------------------------------------------------------------------------------------------------------|
___________________________________________________________________________________________________________________________________|
<CAPTION>
___________________________________________________________________________________________________________________________________
 Table II -- Derivative Securitites Acquired, Disposed of, or Beneficially Owned                                                   |
___________________________________________________________________________________________________________________________________|
1.Title of Derivative |2.Con-  |3.   |4.    |5.Number of De |6.Date Exer|7.Title and Amount  |8.Price|9.Number    |10.|11.Nature of|
  Security            |version |Transaction | rivative Secu |cisable and|  of Underlying     |of Deri|of Deriva   |Dir|Indirect    |
                      |or Exer |     |      | rities Acqui  |Expiration |  Securities        |vative |tive        |ect|Beneficial  |
                      |cise    |     |      | red(A) or Dis |Date(Month/|                    |Secu   |Securities  |(D)|Ownership   |
                      |Price of|     |      | posed of(D)   |Day/Year)  |                    |rity   |Benefi      |or |            |
                      |Deriva- |     |      |               |Date |Expir|                    |       |ficially    |Ind|            |
                      |tive    |     |      |           | A/|Exer-|ation|   Title and Number |       |Owned at    |ire|            |
                      |Secu-   |     |    | |           | D |cisa-|Date |   of Shares        |       |End of      |ct |            |
                      |rity    |Date |Code|V|  Amount   |   |ble  |     |                    |       |Month       |(I)|            |
___________________________________________________________________________________________________________________________________|
<S>                   <C>      <C>   <C>  <C><C>        <C> <C>   <C>   <C>          <C>     <C>     <C>          <C> <C>
                      |        |     |    | |           |   |     |     |            |       |       |            |   |            |
___________________________________________________________________________________________________________________________________|
</TABLE>
Explanation of Responses:
(1) The information reported herein is based on plan balances as of June 30, 
1998.  The information does not 
reflect transactions and holdings subsequent to that date that are eligible for 
deferred reporting on Form 5.
SIGNATURE OF REPORTING PERSON
S. Eugene Edwards
DATE
07/09/98



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