EXHIBIT 23.3 CONSENT OF ELMS, FARIS & CO., P.C. The Board of Directors Costilla Energy, Inc. We consent to incorporation by reference in the registration statements (No. 333-16513, No. 333-16515 and No. 333-16517) on Form S-8 of our report dated March 31, 1995, relating to the consolidated statements of operations, stockholders' equity, and cash flows for the year ended December 31, 1994 of the predecessor entities of Costilla Energy, Inc. and subsidiaries, which report appears in the December 31, 1996, annual report on Form 10-K of Costilla Energy, Inc. ELMS, FARIS & CO., P.C. Midland, Texas March 25, 1997