EXHIBIT 23.1 CONSENT OF KPMG PEAT MARWICK LLP 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 10, 1997, relating to the consolidated balance sheets of Costilla Energy, Inc. and subsidiaries as of December 31, 1996 and 1995, and the related consolidated statements of operations, stockholders' equity, and cash flows for the years then ended, which report appears in the December 31, 1996, annual report on Form 10-K of Costilla Energy, Inc. KPMG PEAT MARWICK LLP Midland, Texas March 26, 1997