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                                                                    EXHIBIT 23.2
 
                        CONSENT OF INDEPENDENT ENGINEERS
 
   
     As independent engineering consultants, we hereby consent to the use of our
reports and data extracted therefrom (and all references to our Firm)
incorporated by reference in or otherwise made a part of this Amendment No. 2 to
Registration Statement on Form S-3 relating to the registration of 3,000,000
shares of the Common Stock, $0.10 par value, of Costilla Energy, Inc. to be
filed with the Securities and Exchange Commission on or about February 10, 1999.
    
 
                                          WILLIAMSON PETROLEUM CONSULTANTS, INC.
 
Houston, Texas
   
February 10, 1999