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                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                                    FORM 8-K

                                 CURRENT REPORT

     Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934

                                  June 3, 1998
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                Date of Report (Date of earliest event reported)

                              COSTILLA ENERGY, INC.
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            (Exact name of registrant as specified in its character)

    Delaware                           0-21411                   75-2658940
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(State or other               (Commission File Number)         (IRS Employer 
  jurisdiction)                                             Identification No.)

                          400 West Illinois, Suite 1000
                              Midland, Texas 79701
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                    (Address of principal executive offices)

                                 (915) 683-3902
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              (Registrant's telephone number, including area code)

                                       N/A
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          (Former name or former address, if changed since last report)



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ITEM 5.  OTHER EVENTS

         On June 3, 1998, Costilla Energy, Inc. (the "Registrant") closed a
private placement of 50,000 shares of its 7% (8% Paid in Kind) Series A
Cumulative Convertible Preferred Stock, $0.10 par value (the "Preferred Stock"),
to Enron Capital & Trade Resources Corp. and Joint Energy Development
Investments II Limited Partnership (the "Purchasers") for a purchase price of
$50.0 million. The Registrant will use the proceeds from the sale to reduce
existing bank debt and for general corporate purposes. A 4% placement fee was
paid to ECT Securities Corp., an affiliate of the Purchasers, in connection with
the transaction.

         The terms, rights and preferences of the Preferred Stock are set forth
in that certain Certificate of Designations of 7% (8% Paid in Kind) Series A
Cumulative Convertible Preferred Stock of Costilla Energy, Inc. (the
"Certificate of Designations"), a copy of which is attached as an exhibit
hereto. The summary of such terms, rights and preferences set forth herein is
qualified in all respects by the more detailed provisions of the Certificate of
Designations.

         The Preferred Stock accrues dividends payable quarterly in cash, or in
certain instances in shares of the Registrant's common stock, $0.10 par value
(the "Common Stock"). The dividend rate is 7% for dividends paid in cash and 8%
for dividends paid in shares of Common Stock. The holders of the Preferred Stock
may, at any time, convert shares of Preferred Stock into shares of the
Registrant's Common Stock at a conversion price of $12.39 (initially equivalent
to the rate of approximately 80.71 shares of Common Stock for each share of
Preferred Stock), subject to adjustment as described in the Certificate of
Designations. Based upon such initial conversion price, the 50,000 shares of
Preferred Stock issued to the Purchasers is convertible into 4,035,513 shares of
Common Stock, which would have constituted approximately 28.8% of the
outstanding Common Stock if such conversion had occurred June 3, 1998. The
Registrant may, at its option, redeem the shares of Preferred Stock after June
15, 2001, subject to certain limitations, for a redemption price equal to the
following percentage of the Liquidation Preference (as defined in the
Certificate of Designations) for a twelve-month period beginning on June 15 of
the year indicated: 2001: 107%; 2002: 103.5%; 2003: 101.75%; 2004 and
thereafter: 100%.

         As more fully set forth in the Certificate of Designations, the holders
of the Preferred Stock are not entitled to any voting rights other than with
respect to certain transfers of substantially all the Registrant's assets
(whether by sale or business combination), items which effect the rights of the
Preferred Stock and issuances of any capital stock senior to or in parity with
the Preferred Stock. However, the holders of the Preferred Stock are entitled to
designate one (increasing to two or more upon occurrence of certain events)
nominee for appointment or election to the Registrant's Board of Directors, and
the Registrant is required to initially make such appointment and to
subsequently use its best efforts to have such nominee elected by the
shareholders. In accordance with this requirement, the Registrant created a new
position on its Board, classified as a Class II director (current term expiring
2001) in the Registrant's staggered Board structure. The newly-created position
has been filled by the appointment of Timothy J. Detmering, the designee of the
Purchasers.



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ITEM 7. FINANCIAL STATEMENTS AND EXHIBITS

         (a) and (b)       No financial statements are required

         (c)               Exhibits

                           4.1      Certificate of Designations of 7% (8% Paid
                                    in Kind) Series A Cumulative Convertible
                                    Preferred Stock of Costilla Energy, Inc.


                                   SIGNATURES

         Pursuant to the requirements of the Securities Exchange Act of 1934,
the Registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.

                                               COSTILLA ENERGY, INC.


June 4, 1998                          By:   /s/ BOBBY W. PAGE
                                           -------------------------------------
                                           Bobby W. Page, Senior
                                           Vice President and
                                           Chief Financial Officer





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                               INDEX TO EXHIBITS



<TABLE>
<CAPTION>
Exhibit                  Description
-------                  -----------
  <S>                    <C>
  4.1                    Certificate of Designations of 7% (8% Paid in Kind)
                         Series A Cumulative Convertible Preferred Stock of 
                         Costilla Energy, Inc.

</TABLE>