<PAGE>   1
                                                                  Rule 424(b)(3)
                                                              File No. 333-33949
                                                          Renal Care Group, Inc.




                    SUPPLEMENT NO. 1 DATED DECEMBER 23, 1997
                      TO PROSPECTUS DATED OCTOBER 14, 1997




         In order to reflect a transfer of 30,000 shares by Janis Birchall,
M.D., the table of Selling Shareholders in the Selling Shareholders section of
the Prospectus is hereby supplemented as follows:

<TABLE>
<CAPTION>               
                                                                                                                  
                           Shares Beneficially                                                 Shares Beneficially
                            Owned Before the                   Shares Being                     Owned After the
Name                          Offering (1)                        Offered                          Offering
- ----                       -------------------               -------------------               -------------------
<S>                        <C>                               <C>                               <C>
The Robert and 
Janis Birchall 
  Foundation                     30,000                            30,000                               --
</TABLE>



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