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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) included
in or made a part of this Registration Statement on Form S-4 relating to the
registration of 10 1/4% Notes due 2006 of Costilla Energy, Inc. to be filed with
the Securities and Exchange Commission on or about April 17, 1998.
 
                                          WILLIAMSON PETROLEUM CONSULTANTS, INC.
 
Houston, Texas
April 17, 1998