<PAGE>   1
================================================================================

                                UNITED STATES
                     SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                          ------------------------

                                  FORM 10-Q

      [X]     Quarterly Report Pursuant to Section 13 or 15(d)
                   of the Securities Exchange Act of 1934
                FOR THE QUARTERLY PERIOD ENDED MARCH 31, 1998

                                     or

      [ ]     Transition Report Pursuant to Section 13 or 15(d)
                   of the Securities Exchange Act of 1934
              For the transition period from _______ to _______

                         COMMISSION FILE NO. 0-21411

                            ------------------------

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

                            ------------------------



         DELAWARE                                               75-2658940
(State or other jurisdiction of                             (I.R.S. Employer
  incorporation or organization)                            Identification No.)

    400 WEST ILLINOIS, SUITE 1000
         MIDLAND, TEXAS                                          79701
(Address of principal executive offices)                       (Zip code)

                               (915) 683-3092
            (Registrant's telephone number, including area code)

                               Not applicable
            (Former name, former address and former fiscal year,
                        if changed since last report)

                            ------------------------

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the Registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.


                         YES  [X]           NO  [ ] 
    


NUMBER OF SHARES OF COMMON STOCK OUTSTANDING AS OF MAY 14, 1998 . . .  9,981,000


================================================================================





<PAGE>   2

                            COSTILLA ENERGY, INC.

                                  FORM 10-Q

                              TABLE OF CONTENTS

                                      

<TABLE>
<CAPTION>
                                                                                                 Page
                                                                                                 ----

                         PART I - FINANCIAL INFORMATION

<S>         <C>                                                                                   <C>
Item 1.    Financial Statements

           Consolidated Balance Sheets as of March 31, 1998 (unaudited) and
               December 31, 1997 .................................................................  3

           Consolidated Statements of Operations for the three months
               ended March 31, 1998 and 1997 (unaudited) .........................................  4

           Consolidated Statements of Cash Flows for the three months
               ended March 31, 1998 and 1997 (unaudited) .........................................  5

           Notes to Consolidated Financial Statements (unaudited) ................................. 6

Item 2.    Management's Discussion and Analysis of Financial
               Condition and Results of Operations ............................................... 10


                           PART II - OTHER INFORMATION


Item 6.    Exhibits and Reports on Form 8-K ...................................................... 16

Signatures........................................................................................ 17

</TABLE>



                                       2




<PAGE>   3

                         PART I - FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS



                              COSTILLA ENERGY, INC.
                           CONSOLIDATED BALANCE SHEETS
                                 (IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                     MARCH 31,      DECEMBER 31,
                                                                        1998           1997
                                                                    -----------     ------------
                                    ASSETS                          (UNAUDITED)
<S>                                                                  <C>            <C>      
CURRENT ASSETS:
   Cash and cash equivalents                                         $   3,473      $   3,615
   Accounts receivable:
       Trade, net                                                        7,019          5,241
       Oil and gas sales                                                 7,623          9,312
   Prepaid and other current assets                                      1,789            912
                                                                     ---------      ---------
           Total current assets                                         19,904         19,080
                                                                     ---------      ---------

PROPERTY, PLANT AND EQUIPMENT, AT COST:
   Oil and gas properties, using the successful efforts
     method of accounting:
       Proved properties                                               221,843        199,355
       Unproved properties                                              41,639         35,971
   Accumulated depletion, depreciation and amortization                (76,577)       (71,152)
                                                                     ---------      ---------

                                                                       186,905        164,174
   Other property and equipment, net                                     3,684          3,766
                                                                     ---------      ---------

           Total property, plant and equipment                         190,589        167,940
                                                                     ---------      ---------

OTHER ASSETS:
   Deferred charges                                                      6,917          4,212
   Other                                                                 2,333          2,856
                                                                     ---------      ---------
           Total other assets                                            9,250          7,068
                                                                     ---------      ---------

                                                                     $ 219,743      $ 194,088
                                                                     =========      =========

       LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT LIABILITIES:
   Current maturities of long-term debt                              $      98      $      98
   Trade accounts payable                                               22,002         22,490
   Undistributed revenue                                                 3,271          4,566
   Other current liabilities                                             7,736          3,437
                                                                     ---------      ---------

           Total current liabilities                                    33,107         30,591
                                                                     ---------      ---------

LONG-TERM DEBT, LESS CURRENT MATURITIES                                195,519        163,087
                                                                     ---------      ---------
OTHER NONCURRENT LIABILITIES                                               185           --
                                                                     ---------      ---------


STOCKHOLDERS' EQUITY :
   Preferred stock, $.10 par value (3,000,000 shares authorized;
     no shares outstanding)                                               --             --
   Common stock, $.10 par value (20,000,000 shares authorized;
     9,981,000 shares outstanding at March 31, 1998 and
     10,150,500 shares outstanding at December 31, 1997)                   998          1,015
   Additional paid-in capital                                           35,600         37,425
   Retained deficit                                                    (45,666)       (38,030)
                                                                     ---------      ---------

           Total stockholders' equity                                   (9,068)           410
                                                                     ---------      ---------

COMMITMENTS AND CONTINGENCIES                                             --             --
                                                                     ---------      ---------

                                                                     $ 219,743      $ 194,088
                                                                     =========      =========
</TABLE>



See accompanying notes to consolidated financial statements.



                                       3



<PAGE>   4





                              COSTILLA ENERGY, INC.

                      CONSOLIDATED STATEMENTS OF OPERATIONS
                      (IN THOUSANDS, EXCEPT PER SHARE DATA)
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                                          THREE MONTHS ENDED
                                                                              MARCH 31,
                                                                         ----------------------
                                                                           1998          1997
                                                                         --------      --------
<S>                                                                      <C>           <C>     
REVENUES:
  Oil and gas sales                                                      $ 15,345      $ 19,613
  Interest and other                                                          205           795
  Gain on sale of assets                                                      337           (30)
                                                                         --------      --------

                                                                           15,887        20,378
                                                                         --------      --------

EXPENSES:

  Oil and gas production                                                    6,785         7,369
  General and administrative                                                2,493         1,515
  Exploration and abandonments                                              3,151         1,340
  Depreciation, depletion and amortization                                  6,059         4,914
  Interest                                                                  4,739         2,708

                                                                         --------      --------

                                                                           23,227        17,846
                                                                         --------      --------

    Income (loss) before federal income taxes and extraordinary item       (7,340)        2,532
PROVISION FOR FEDERAL INCOME TAXES
  Current                                                                    --              62
  Deferred                                                                   --             191
                                                                         --------      --------

    Income (loss) before extraordinary item                                (7,340)        2,279

    Extraordinary loss resulting from early extinguishment of debt           (299)         --
                                                                         --------      --------


NET INCOME (LOSS)                                                        $ (7,639)     $  2,279
                                                                         ========      ========

INCOME (LOSS)  PER SHARE:
  Income (loss) before extraordinary item                                $  (0.73)     $   0.22


  Extraordinary loss resulting from early extinguishment of debt            (0.03)         --
                                                                         --------      --------

  NET INCOME (LOSS)                                                      $  (0.76)     $   0.22
                                                                         ========      ========


WEIGHTED AVERAGE SHARES OUTSTANDING                                        10,073        10,476
                                                                         ========      ========
</TABLE>


See accompanying notes to consolidated financial statements.



                                        4


<PAGE>   5


                              COSTILLA ENERGY, INC.

                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (IN THOUSANDS)
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                                          THREE MONTHS ENDED
                                                                               MARCH 31,
                                                                         ----------------------
                                                                           1998          1997
                                                                         --------      --------
<S>                                                                      <C>           <C>     
CASH FLOWS FROM OPERATING ACTIVITIES:

   NET INCOME (LOSS)                                                     $ (7,639)     $  2,279

   ADJUSTMENTS TO RECONCILE NET INCOME (LOSS) TO NET
      CASH PROVIDED BY OPERATING ACTIVITIES:

      Depreciation, depletion and amortization                              6,059         4,914
      Impairment of oil and gas properties                                   --            --
      Exploration and abandonments                                            194            47
      Amortization of deferred charges                                         97           151
      Deferred income tax expense                                            --             191
      Gain on sale of oil and gas properties                                 (337)           30
      Extraordinary loss resulting from early extinguishment of debt          299          --
      Gain on investment transactions                                          (5)         (757)
                                                                         --------      --------

                                                                           (1,332)        6,855

      Changes in operating assets and liabilities:
        Decrease (increase) in accounts receivable                            (89)         (621)
        Decrease (increase) in other assets                                  (410)         (407)
        Increase (decrease) in accounts payable                            (1,783)        5,015
        Increase (decrease) in other liabilities                            4,489         2,618
                                                                         --------      --------

            Net cash provided by operating activities                         875        13,460
                                                                         --------      --------

CASH FLOWS FROM INVESTING ACTIVITIES:

   Additions to oil and gas properties                                    (30,768)      (15,207)
   Proceeds from sale of oil and gas properties                             2,500           867
   Additions to other property and equipment                                 (198)         (671)

                                                                         --------      --------

            Net cash used in investing activities                         (28,466)      (15,011)
                                                                         --------      --------

CASH FLOWS FROM FINANCING ACTIVITIES:

   Borrowings under long-term debt                                         95,000          --
   Payments of long-term debt                                             (62,520)          (18)
   Proceeds from issuance of common stock, net                               --              14
   Purchase of common stock                                                (1,841)         --
   Deferred loan and financing costs                                       (3,190)          (61)
                                                                         --------      --------

            Net cash provided by (used in) financing activities            27,449           (65)
                                                                         --------      --------

NET INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS                         (142)       (1,616)

CASH AND CASH EQUIVALENTS, BEGINNING OF PERIOD                              3,615        12,618
                                                                         --------      --------

CASH AND CASH EQUIVALENTS, END OF PERIOD                                 $  3,473      $ 11,002
                                                                         ========      ========
</TABLE>



See accompanying notes to consolidated financial statements.





                                        5


<PAGE>   6



                              COSTILLA ENERGY, INC.


                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                 MARCH 31, 1998
                                   (UNAUDITED)



1. SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

         The interim financial information as of March 31, 1998, and for the
three months ended March 31, 1998 and 1997, is unaudited. Certain information
and footnote disclosures normally included in financial statements prepared in
accordance with generally accepted accounting principles have been condensed or
omitted in this Form 10-Q pursuant to the rules and regulations of the
Securities and Exchange Commission. However, in the opinion of management, these
interim financial statements include all the necessary adjustments to fairly
present the results of the interim periods and all such adjustments are of a
normal recurring nature. The interim consolidated financial statements should be
read in conjunction with the audited financial statements for the year ended
December 31, 1997.

         Costilla Energy, Inc. ("Costilla" or the "Company") was incorporated in
Delaware in June 1996 to consolidate and continue the activities previously
conducted by Costilla Energy, L.L.C., a Texas limited liability company (the
"LLC"), and its wholly owned subsidiaries, to acquire the assets of CSL
Management Corporation (which owned certain office equipment used by the
Company), and to acquire the stock of Valley Gathering Company. Costilla was
formed for the purpose of conducting a $60 million initial public offering of
common stock and a $100 million senior notes offering (the "Offerings"), which
Offerings were completed in early October 1996.

         The Company is an oil and gas exploration and production concern with
properties located principally in South and East Texas, the Rocky Mountains and
the Permian Basin regions of the United States.


2. DERIVATIVE FINANCIAL INSTRUMENTS

         The Company utilizes derivative financial instruments to manage
well-defined interest rate and commodity price risks. The Company is exposed to
credit losses in the event of nonperformance by the counterparties to its
interest rate swap agreements and its commodity hedges. The Company only deals
with reputable financial institutions as counterparties and anticipates that
such counterparties will be able to fully satisfy their obligations under the
contracts. The Company does not obtain collateral or other security to support
financial instruments subject to credit risk but monitors the credit standing of
the counterparties.


         Commodity Hedges. The Company utilizes option contracts to hedge the
effect of price changes on future oil and gas production. If market prices of
oil and gas exceed the strike price of put options, the options will expire
unexercised, therefore reducing the effective price received for oil and gas
sales by the cost of the related put option. If market prices of oil and gas
exceed the strike price of call options, the Company is obligated to pay the
contracting counterparty an amount equal to the contracted volumes times the
difference between the market price and the strike price, therefore, reducing
the effective price received for oil and gas sales by the amount paid to the
counterparty.


                                        6


<PAGE>   7



         The following table sets forth the future volumes hedged by year and
the strike prices of the option contracts at March 31, 1998:


<TABLE>
<CAPTION>
                                            OIL                 GAS
                                          VOLUME               VOLUME               STRIKE PRICE     
                                          (BBLS)              (MMBTU)               PER BBL/MMBTU    
                                        ------------       ---------------       ------------------ 
<S>                                     <C>               <C>                    <C>       
   Oil:                                                                                              

       1998 (through August, 1998)          994,500                     -         $18.50 - $22.55(a) 
   Gas:                                                                                              
       1998 (through October, 1998)               -             1,070,000              $2.00(b)         
       1998 (through October, 1998)               -             8,560,000         $2.40(c) - $2.55(a)   
</TABLE>

--------------------

         (a)   Represents the strike prices of a collar established with the 
               purchase of a put option contract and the sale of a call option 
               contract. 
         (b)   Represents the strike price on purchased put option contracts.
         (c)   $2.15 per Mmbtu for April 1998.

         Interest Rate Swap Agreements. Prior to the Offerings, the Company
utilized two interest rate swap agreements to reduce the potential impact of
increases in interest rates on floating-rate long-term debt. Concurrent with the
issuance of the $100 million of 10.25% fixed-rate senior notes in early October
1996, the two interest rate swap agreements ceased to be hedges. These interest
rate swap agreements were marked-to-market and the related liability recorded.
The liability for the two interest rate swap agreements was $1,712,000 at
December 31, 1996. A $60 million interest rate swap agreement expired in May
1997. As a result of the Company's borrowings against its line of credit, which
bears interest on a floating rate basis, the remaining $24 million interest rate
swap agreement again fully qualified as a hedge in August 1997. At each
borrowing date from October 1996 to August 1997, a portion of the interest rate
swap agreement was marked-to-market with the resulting gains or losses recorded
as investment income or loss while the hedge portion was being amortized over
the remaining life of the agreement. As a result of marking the agreements to
market, the Company recorded net investment gains of approximately $4,000 and
$541,000 for the three months ended March 31, 1998 and 1997, respectively.
Concurrent with the payment of all of the Company's floating rate debt from
proceeds of the 1998 Notes (as defined and discussed in Note 4), the interest
rate swap agreement ceased to qualify as a hedge. As a result of
marking-to-market the interest rate swap agreement at that time, the Company
recorded an additional liability of approximately $23,000. The interest rate
swap agreement in place as of March 31, 1998 has a notional amount of $24
million with a fixed rate of 7.5% and will expire in January, 1999. As of March
31, 1998, the carrying value of the interest swap agreement was a liability of
approximately $422,000.


3. ACQUISITIONS

         On August 28, 1997, the Company consummated the purchase from Ballard
Petroleum LLC ("Ballard") of certain oil and gas properties for an estimated
adjusted purchase price of approximately $41.2 million (the "Ballard
Acquisition"). The properties are located primarily in the Rocky Mountain region
of the United States. The transaction was accounted for using the purchase
method. The results of operations of the acquired properties are included in the
Consolidated Statements of Operations as of the acquisition closing date, August
28, 1997. In addition, the Company and Ballard have entered into an Acquisition
and Exploration Agreement that establishes an area of mutual interest in the
Rocky Mountain Region in which the parties will jointly own, acquire, explore
and develop properties.



                                        7


<PAGE>   8



         Pro Forma Results of Operations

         The following table reflects the pro forma results of operations for
the three months ended March 31, 1997, as though the Ballard Acquisition
occurred as of January 1, 1997. The pro forma amounts are not necessarily
indicative of results that may be reported in the future.


<TABLE>
<CAPTION>
                                                          THREE MONTHS ENDED
                                                              MARCH 31, 1997
                                                          ----------------------
                                                              (in thousands)
<S>                                                             <C>     
Revenues                                                        $ 23,440
Net income before extraordinary items                              1,588
Net income per share before extraordinary items                 $   0.15
</TABLE>


4. LONG TERM DEBT

         In August 1997, the Company entered into a credit agreement (the
"Revolving Credit Facility") with Bankers Trust Company, as agent, to refinance
its existing bank indebtedness and to finance a portion of the Ballard
Acquisition purchase price. The Revolving Credit Facility provides for a maximum
availability of $75.0 million, $13.5 million of which was borrowed at March 31,
1998 against an available borrowing base of $40.0 million at such date.
Borrowings under the Revolving Credit Facility bear interest, at the Company's
option, at a floating rate which is at or above the Lender's prime rate or above
the applicable Eurodollar rate, depending on the percentage of committed funds
which have been borrowed. Interest is payable quarterly as to base rate loans,
and at the end of the applicable interest period as to Eurodollar loans. The
borrowing base of the Revolving Credit Facility is automatically reduced by 5%
each quarter beginning in August 1999, and payments of principal are required in
each quarter in which the outstanding principal balance is greater than the
reduced borrowing base. The remaining balance is payable on August 28, 2002, the
maturity date of the Revolving Credit Facility. Under the Revolving Credit
Facility, the Company is obligated to pay certain fees to the lender, including
a commitment fee based on the unused portion of the commitment. The Revolving
Credit Facility contains customary restrictive covenants (including restrictions
on the payment of dividends and the incurrence of additional indebtedness) and
requires the Company to maintain (i) a current ratio of not less than 1.0 to
1.0, including amounts available under the Revolving Credit Facility and
excluding current maturities under the Revolving Credit Facility and the
Acquisition Credit Facility, (ii) a ratio of EBITDA to interest expense of not
less than 2.50 to 1 and (iii) a minimum tangible net worth. Borrowings under the
Revolving Credit Facility are secured by substantially all of the assets of the
Company.

         Contemporaneous with entering into the Revolving Credit Facility, the
Company also entered into a second credit agreement (the "Acquisition Credit
Facility") to provide the remaining financing for the Ballard Acquisition. The
Acquisition Credit Facility was a term loan in the amount of $30.0 million which
was repaid in full in connection with the sale of the 1998 Notes.

         In October 1996, the Company issued $100 million aggregate principal
amount of 10.25% Senior Notes due October 1, 2006 (the "Notes"). The Notes were
sold at par and interest is payable April 1 and October 1, commencing April 1,
1997. The Notes may not be redeemed prior to October 1, 2001, and thereafter at
a premium reducing to par, plus interest, by maturity. There is no mandatory
redemption of the Notes required prior to maturity. The Notes are general
unsecured senior obligations of the Company and rank equally in right of payment
with all other senior indebtedness of the Company and senior in right of payment
of all existing future subordinated indebtedness of the Company. The Notes are
subject to an Indenture between the Company and a trustee. The Indenture
restricts, among other things, the Company's ability to incur additional
indebtedness, pay dividends or make certain other restricted payments, incur
liens, engage in any sale and leaseback transaction, sell stock of subsidiaries,
apply net proceeds from certain assets sales, merge or consolidate with any
other person, sell, assign, transfer, lease, convey or otherwise dispose of
substantially all of the assets of the company, or enter into certain
transactions with affiliates. Net proceeds from the sale of the Notes of
approximately $96.1 million were used to repay existing indebtedness.


                                       8
<PAGE>   9

         In January 1998, the Company issued an additional $80 million aggregate
principal amount of 10.25% Senior Notes due October 1, 2006 (the " 1998 Notes").
The notes were sold at a premium (102.5%) and interest is payable April 1 and
October 1, commencing April 1, 1998. The 1998 Notes may not be redeemed prior to
October 1, 2001, and thereafter at a premium reducing to par, plus interest, by
maturity. The 1998 Notes are subject to the same terms and conditions as the
Notes. Net proceeds from the sale of the 1998 Notes of approximately $78.8
million were used to repay the Acquisition Credit Facility in full, all but
$500,000 of the Revolving Credit Facility and the remainder was used for general
corporate working capital needs.


5.  REPORTING COMPREHENSIVE INCOME

         In June 1997, the FASB issued Statement of Accounting Standards No. 130
"Reporting Comprehensive Income" ("FAS 130") which establishes standards for
reporting and display of comprehensive income and its components in a full set
of general-purpose financial statements. Specifically, FAS 130 requires that an
enterprise (i) classify items of other comprehensive income by their nature in a
financial statement and (ii) display the accumulated balance of other
comprehensive income separately from retained earnings and additional paid-in
capital in the equity section of a statement of financial position. This
statement is effective for fiscal years beginning after December 15, 1997. The
Company has adopted the provisions of FAS 130 in its consolidated financial
statements for periods ending after December 31, 1997. The Company had no
financial instruments giving rise to comprehensive income during the three
months ended March 31, 1998.

         Comprehensive income consists of the change in equity of a business
enterprise during a period from transactions and other events and circumstances
from nonowner sources. Specifically, this includes net income and other
comprehensive income, which is made up of certain changes in assets and
liabilities that are not reported in a statement of operations but are included
in the balances within a separate component of equity in a statement of
financial position. Such changes include, but are not limited to, unrealized
gains for marketable securities and future contracts, foreign currency
translation adjustments and minimum pension liability adjustments.



                                       9

<PAGE>   10



                              COSTILLA ENERGY, INC.


                SPECIAL NOTE REGARDING FORWARD-LOOKING STATEMENTS


         Certain statements in this Form 10-Q constitute "forward-looking
statements" within the meaning of the Private Securities Litigation Reform Act
of 1995 (the "Reform Act"). Such forward-looking statements involve known and
unknown risks, uncertainties, and other factors which may cause the actual
results, performance, or achievements of Costilla to be materially different
from any future results, performance, or achievements expressed or implied by
such forward-looking statements. Such factors include, among others, the
following: the volatility of oil and gas prices, the Company's drilling results
and ability to replace oil and gas reserves, the availability of capital
resources, the reliance upon estimates of proved reserves, operating hazards and
uninsured risks, competition, government regulation, and the ability of the
Company to implement its business strategy, and other factors referenced in the
Company's public filings with the Securities and Exchange Commission.



ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
         OF OPERATIONS

GENERAL

         Costilla is an independent energy company engaged in the exploration,
acquisition and development of oil and gas properties. The Company's predecessor
began operating in 1988 and through mid-1995 had grown primarily through a
series of small acquisitions of oil and gas properties and the exploitation of
those properties. In June 1995, Costilla consummated the acquisition of certain
oil and gas properties for a purchase price of approximately $46.6 million (the
"1995 Acquisition"), in June 1996, Costilla consummated the acquisition of
certain oil and gas properties for a purchase price of approximately $38.7
million (the "1996 Acquisition") and in August 1997, Costilla consummated the
Ballard Acquisition for a purchase price of approximately $41.2 million .

         The Company's strategy is to utilize its technical staff and
technological advances to increase its oil and gas reserves, production and cash
flow from operations through an active exploration program and the acquisition
and development of proved reserves. In addition, Costilla continues to evaluate
the acquisition of undeveloped acreage for its exploration efforts. Costilla has
in-house exploration expertise using 3-D seismic technology to identify new
drilling opportunities as well as for the development of acquired properties.

         The Company has grown primarily through acquisitions which impacted its
reported financial results in a number of ways. Properties sold by others
frequently have not received focused attention prior to sale. After acquisition,
certain of these properties are in need of maintenance, workovers, recompletions
and other remedial activity not constituting capital expenditures, which
substantially increase lease operating expenses. The increased production and
revenue resulting from these expenditures is predominately realized in periods
subsequent to the period of expense. In addition, the rapid growth of the
Company has required it to develop operating, accounting and administrative
personnel compatible with its increased size. The Company believes it has now
achieved a sufficient size to expand its reserve base without a corresponding
increase in its general and administrative expense. The Company also believes it
now has a sufficient inventory of prospects and the professional staff necessary
to follow a more balanced program of exploration and development activities to
complement its acquisition efforts.



                                       10


<PAGE>   11



         The following table sets forth certain operating data of Costilla for
the periods presented:


<TABLE>
<CAPTION>
                                                      Three Months Ended
                                                           March 31,
                                                     ---------------------
                                                       1998          1997
                                                     --------      -------
<S>                                                  <C>           <C>   
OIL AND GAS PRODUCTION:
    Oil (Mbbls)                                           544          547   
    Gas (Mmcf)                                          3,432        3,285   
    MBOE(1)                                             1,116        1,095   
                                                                             
AVERAGE SALES PRICES (2):                                                    
    Oil  (per Bbbl)                                   $ 15.37      $ 19.84  
    Gas (per Mcf)                                        2.03         2.67   
                                                                             
COSTS PER BOE (1):                                                           
    Production  cost                                  $  6.08      $  6.74   
    Depreciation, depletion and amortization             5.43         4.49   
    General and administrative                           2.23         1.38
</TABLE>

-------------

(1) BOE represents equivalent barrels of oil.  In reference to natural gas, 
    natural gas equivalents are determined using the ratio of six Mcf of natural
    gas to one barrel of crude oil, condensate or natural gas liquids. MBOE 
    represents one thousand barrels of oil equivalent.
(2) Before deduction of production taxes and including any hedging results.


         Costilla uses the successful efforts method of accounting for its oil
and gas activities. Costs to acquire mineral interests in oil and gas
properties, to drill and equip exploratory wells that result in proved reserves,
and to drill and equip development wells are capitalized. Costs to drill
exploratory wells that do not result in proved reserves, geological, geophysical
and seismic costs, and costs of carrying and retaining unproved properties are
expensed. Capitalized costs of producing oil and gas properties, after
considering estimated dismantlement and abandonment costs and estimated salvage
values, are depreciated and depleted using the unit-of-production method.
Unproved oil and gas properties that are individually significant are
periodically reviewed for impairment of value, and a loss is recognized at the
time of impairment by providing an impairment allowance. Other unproved
properties are amortized based on the Company's experience of successful
drilling and average holding period.


         The Company utilizes option contracts to hedge the effect of price
changes on a portion of its future oil and gas production. Premiums paid and
amounts receivable under the option contracts are amortized and accrued to oil
and gas sales, respectively. If market prices of oil and gas exceed the strike
price of put options, the options will expire unexercised, therefore, reducing
the effective price received for oil and gas sales by the cost of the related
option. Conversely, if market prices of oil and gas decline below the strike
price of put options, the options will be exercised, therefore, increasing the
effective price received for oil and gas sales by the proceeds received from the
related option. If market prices of oil and gas exceed the strike price of call
options, the Company is obligated to pay the contracting counterparty an amount
equal to the contracted volumes times the difference between the market price
and the strike price, therefore, reducing the effective price received for oil
and gas sales by the amount paid to the counterparty. The net effect of the
Company's commodity hedging activities increased oil and gas revenues by
$1,437,000 for the three months ended March 31, 1998 and reduced oil and gas
revenues by $510,000 for the comparable period in 1997. The Company has
purchased put options on 6,500 Bbls of oil per day which establish a floor price
of $18.50 per Bbl and sold call options on 6,500 Bbls of oil per day at $22.55
per Bbl. These oil option contracts continue through August 1998. The referenced
oil prices are based upon the price at which West Texas Intermediate crude oil
("WTI") trades on the New York Mercantile Exchange ("NYMEX"). The Company has
historically received a gross wellhead sales price for oil of approximately 82 -
90% of the NYMEX price. The Company has also purchased put options on 5,000
Mmbtu of gas per day which provide for a floor of $2.00 per Mmbtu through
October 1998. Additionally, the Company has purchased put options on 40,000
Mmbtu of gas per day which establish a floor price of $2.40 per Mmbtu ($2.15 per
Mmbtu for April 1998) and sold call options on 40,000 Mmbtu of gas per day at
$2.55 per Mmbtu. These gas option contracts are for the period April 1998
through October 1998. The referenced gas prices are based upon the index price
for Houston Ship Channel gas sales, which is approximately 97% of NYMEX. The
Company has historically received a gross wellhead sales price for gas of
approximately 87 - 90% of NYMEX.


                                    11
<PAGE>   12
         The Company utilizes interest rate swap agreements to reduce the
potential impact of increases in interest rates on floating-rate, long term
debt. If market rates of interest experienced during the applicable swap term
are below the rate of interest effectively fixed by the swap agreement, the rate
of interest incurred by the Company will exceed the rate that would have been
experienced under its then outstanding floating-rate indebtedness. The net
effect of the Company's interest rate hedging activities increased interest
expense by approximately $3,000 and $31,000 for the three months ended March 31,
1998 and 1997, respectively. Concurrent with the payment of all of the Company's
floating rate debt from proceeds of the initial public offering and the notes
offering consummated in the fourth quarter of 1996, the interest rate swap
agreements ceased to qualify as hedges. These interest rate swap agreements were
marked-to-market and the related liability of $1,712,000 was recorded. A $60
million interest rate swap expired in May 1997. As a result of the Company's
borrowings against its line of credit, which bears interest on a floating rate
basis, the remaining $24 million interest rate swap agreement again qualified as
a hedge beginning in August 1997. At each borrowing date from October 1996 to
August 1997, a portion of the interest rate swap agreement was marked-to-market
with the resulting gains or losses recorded as investment income or loss while
the hedge portion is being amortized over the remaining life of the agreement.
As a result of marking the agreements to market, the Company recorded net
investment gains of approximately $4,000 and $541,000 during the three months
ended March 31, 1998 and 1997, respectively. Concurrent with the payment of all
of the Company's floating rate debt from proceeds of the notes offering in
January 1998, the interest rate swap agreement ceased to qualify as a hedge. As
a result of marking-to-market the interest rate swap agreement in January 1998,
the Company recorded an additional liability of approximately $23,000. As of
March 31, 1998, the carrying value of the interest swap agreement was a
liability of approximately $422,000.


RESULTS OF OPERATIONS


Three Months Ended March 31, 1998 Compared to Three Months Ended March 31, 1997

         The Company's oil and gas revenues for the three months ended March 31,
1998 were $15,345,000, representing a decrease of $4,268,000 (22%) from revenues
of $19,613,000 in 1997. Lower commodity prices accounted for a decrease in
revenues of $4,553,000 which was partially offset by a combination of successful
drilling activities and revenues related to properties purchased or sold. The
average oil price per barrel received in 1998 was $15.37 compared to $19.84 in
1997, a 22% decrease, and the average gas price received in 1998 was $2.03
compared to $2.67 in 1997, a 24% decrease.

         Oil and gas production was 1,116 MBOE in 1998 compared to 1,095 MBOE in
1997, a 2% increase. Additional production from a combination of successful
drilling activities and acquired properties was largely offset by production
related to properties sold.

         Interest and other revenues were $205,000 for the three months ended
March 31, 1998, representing a $590,000 decrease (75%) compared to $795,000 in
1997. Of this decrease, $143,000 was related to decreased interest income due to
decreased funds earning interest. Gains on investment transactions of $4,000 and
$541,000 were recorded for the three months ended March 31, 1998 and 1997,
respectively. These gains related to an interest rate swap contract which was
marked-to-market.

         Gain on sale of assets was $337,000 for the three months ended March
31, 1998 compared to a loss of $30,000 for 1997, representing an increase of
$367,000 (1,213%). Gains from the sale of certain oil and gas properties
increased by approximately $367,000.


                                       12
<PAGE>   13

         Oil and gas production costs for the three month period ended March 31,
1998 were $6,785,000 ($6.08 per BOE), compared to $7,369,000 in 1997 ($6.74 per
BOE), representing a decrease of $584,000 (8%), due principally to lower
production costs on newly completed wells and the sale of certain oil and gas
properties.

         General and administrative expenses for the three months ended March
31, 1998 were $2,493,000, representing an increase of $978,000 (68%) from 1997
of $1,515,000. The increase is primarily due to an increase in personnel and
related costs necessary to accommodate the increase in the Company's oil and gas
activities, including the Acquisition and Exploration Agreement with Ballard
Petroleum.

         Exploration and abandonment expense increased to $3,151,000 for the
three months ended March 31, 1998 compared to $1,340,000 in 1997. Dry hole and
abandonment costs increased to $2,693,000 in 1998 from $1,120,000 in 1997. The
Company incurred $290,000 of seismic costs for the three months ended March 31,
1998, compared to $80,000 in the comparable period in 1997. The Company incurred
$168,000 of other geological and geophysical costs during the three month period
ended March 31, 1998 compared to $140,000 for the same period in 1997. The
increase in exploration and abandonments expense was primarily related to the
Company's increased exploratory drilling activities in 1998 compared to 1997.

         Depreciation, depletion and amortization ("D D & A") expense for the
three month period ended March 31, 1998 was $6,059,000 compared to $4,914,000
for 1997, representing an increase of $1,145,000 (23%). During the 1998 period,
D D & A on oil and gas production was provided at an average rate of $5.43 per
BOE compared to $4.49 per BOE for 1997. Of the $1,145,000 (23%) increase,
$1,029,000 was due to the $0.94 per BOE increase in D D & A rate necessitated by
lower oil and gas prices at March 31, 1998 than those experienced at March 31,
1997.

         Interest expense was $4,739,000 for the three months ended March 31,
1998, compared to $2,708,000 for the comparable period in 1997. The $2,031,000
(75%) increase was attributable to a combination of higher levels of average
outstanding indebtedness including the issuance in January 1998 of an additional
$80 million of 10.25% senior notes due in 2006. The average amounts of
applicable interest-bearing debt in 1998 and 1997 were $181,461,000 and
$100,253,000, respectively. The effective annualized interest rate in 1998 was
10.6%, as compared to 9.9% in 1997.

         Results of operations for the three months ended March 31, 1998 include
an extraordinary charge of $299,000. There were no extraordinary charges for the
comparable period in 1997. These extraordinary charges related to the early
extinguishment of the Acquisition Credit Facility and consisted of previously
capitalized debt issuance costs. A portion of the proceeds from the 1998 Notes
was used to repay the Acquisition Credit Facility.


LIQUIDITY AND CAPITAL RESOURCES

Net Cash Provided By Operating Activities

         For the three months ended March 31, 1998, net cash provided by
operating activities decreased to $0.9 million from $13.5 million for 1997. Cash
provided by operations, before changes in operating assets and liabilities,
decreased to a negative $1.3 million from $6.9 million for the comparable period
in 1997 due primarily to lower oil and gas prices and exploratory dry holes.

Net Cash Used in Investing Activities

         Net cash used in investing activities for the three months ended March
31, 1998 was $28.5 million. Approximately $11.8 million was used for the 
acquisition of oil and gas properties, with $10.2 million going to Manti
Resources ("Manti Acquisition"), $19.0 million was used for exploration and
development activities and $0.2 million for other property and equipment.
Proceeds from the sale of various oil and gas assets resulted in net cash
provided from investing activities of approximately $2.5 million. For the three
months ended March 31, 1997, net cash used in investing activities was $15.0
million. Approximately $15.2 million was used for exploration and development
activities, $0.7 million was used for other property and $0.9 million was
provided by sales of oil and gas properties.


                                       13

<PAGE>   14

Financing Activities

         For the three months ended March 31, 1998, the Company incurred $95.0
million of debt, of which approximately $62.5 million was used to repay certain
prior bank debt, $10.2 million was used for the Manti Acquisition and the
remainder was used in connection with its exploration and development
activities. In addition, the Company used approximately $1.8 million for the
purchase of 169,500 shares of its common stock. No material financing
transactions occurred during the three months ended March 31, 1997.

         The Company entered into the Revolving Credit Facility in August 1997.
Approximately $19.9 million of the funds initially borrowed were used for the
extension and refinancing of a prior senior credit facility and $11.2 million
was used as a portion of the purchase price in the Ballard Acquisition. The
Revolving Credit Facility provides for a maximum availability of $75.0 million,
with an current borrowing base of $40.0 million, $13.5 million of which was
borrowed at March 31, 1998. Borrowings under the Revolving Credit Facility bear
interest, at the Company's option, at a floating rate which is at or above the
lender's prime rate or above the applicable Eurodollar rate, depending on the
percentage of committed funds which have been borrowed. Interest is payable
quarterly as to base rate loans, and at the end of the applicable interest
period as to Eurodollar rate loans. The borrowing base of the Revolving Credit
Facility is automatically reduced by 5% each quarter beginning in August 1999,
and payments of principal are required in each such quarter in which the
outstanding principal balance is greater than the reduced borrowing base. The
remaining balance is payable on August 31, 2002, the maturity date of the
Revolving Credit Facility.

         Contemporaneous with entering into the Revolving Credit Facility, the
Company also entered into the Acquisition Credit Facility to provide the
remaining financing for the Ballard Acquisition. The Acquisition Credit Facility
was a term loan in the amount of $30.0 million which was repaid in full in
connection with the sale of notes by the Company described in the following
paragraph.

         In January 1998 the Company issued $80 million of 10.25% Senior Notes
due 2006 (the "Supplemental Notes Offering"). The net proceeds of the
Supplemental Notes Offering were approximately $78.8 million. The Company used
$30.0 million to repay the Acquisition Credit Facility and $32.5 million to
repay all but $0.5 million of the Revolving Credit Facility. In mid-January 1998
approximately $10.0 million of the remaining proceeds were used to fund the
Manti Acquisition.


Capital Resources

         Funding for the Company's business activities has historically been
provided by bank financings, cash flow from operations, equity sales, property
divestitures and joint ventures with industry participants. The 1995
Acquisition, 1996 Acquisition and Ballard Acquisition were substantially funded
by bank financings. The Company plans to execute its business strategy with cash
flow from operations, net proceeds from the Supplemental Notes Offering and
borrowings available under the Revolving Credit Facility.

         While the Company regularly engages in discussions relating to
potential acquisitions, the Company has no present agreement, commitment or
understanding with respect to any such acquisition, other than the acquisition
of undeveloped acreage and various mineral interests in its normal course of
business. Any future acquisition may require additional financing and will be
dependent upon financing arrangements available at the time.

         The Company believes that the increased availability under the
Revolving Credit Facility resulting from the application of net proceeds of the
Supplemental Notes Offering and cash flow from operations will be sufficient for
its 1998 capital expenditures. However, because the Company's ultimate 1998
capital expenditures, future cash flows and the availability of financing are
subject to a number of variables, there can be no assurance that the Company's
capital resources will be sufficient to maintain its capital expenditures. In
addition, if the Company is unable to generate sufficient cash flow from
operations to service its debt, it may be required to refinance all or a portion
of its debt or to obtain additional financing. There can be no assurance that
any such refinancing would be possible or that any additional financing could be
obtained.

         Although certain of the Company's costs and expenses may be affected by
inflation, inflationary costs have not had a significant effect on the Company's
results of operations.



                                       14


<PAGE>   15

         Since December 31, 1997 oil and gas prices have continued to
deteriorate. The Company estimates that its cash flow would be reduced by $1.9
million and $2.1 million for each $1 per barrel reduction in the price of oil
and for each $0.10 per Mcf reduction in the price of gas, respectively.


Capital Expenditures

         During the three months ended March 31, 1998 the Company had oil and
gas expenditures of approximately $22.1 million, exclusive of the $11.8 million
spent on the acquisition of existing oil and gas properties. The remaining $22.1
million of oil and gas expenditures consisted of $8.7 million of exploration
costs, $10.3 million of development costs and $3.1 million of undeveloped
acreage. The Company's oil and gas expenditures during the three months ended
March 31, 1998 are not indicative of expenditures for the entire year,
particularly given the current low level of oil prices. In view of the Company's
extensive undeveloped acreage and seismic inventory, it has elected to
temporarily defer non-drilling activities pending an improvement in oil prices.
In addition, the Company intends to concentrate its drilling activities on gas
prospects. Since a significant portion of the Company's 1998 capital budget is
discretionary, the Company is able to increase or decrease its level of activity
as product prices warrant.


Recent Accounting Pronouncements

         INFORMATION SYSTEMS FOR THE YEAR 2000 - The Company will be required to
modify its information systems in order to accurately process data referencing
the year 2000. Because of the importance of occurrence dates in the oil and gas
industry, the consequences of not pursuing these modifications could be very
significant to the Company's ability to manage and report operating activities.
The Company's third-party software vendor for its integrated oil and gas
information system is currently modifying the system to accurately handle the
Year 2000 issue. All necessary programming modifications are scheduled to be
completed by December 31, 1998. From a cost viewpoint, these modifications will
be part of the routine updates the Company receives from its third-party
software vendor as part of its systems support contract already in place. Thus,
the Company believes it will not incur any marginal costs with respect to the
Year 2000 issue.

         SEGMENT REPORTING - In June 1997, the FASB issued Statement of
Accounting Standards No. 131 "Disclosures about Segments of an Enterprise and
Related Information" ("FAS 131") which establishes standards for public business
enterprises for reporting information about operating segments in annual
financial statements and requires that such enterprises report selected
information about operating segments in interim financial reports issued to
shareholders. This statement also established standards for related disclosures
about products and services, geographic areas, and major customers. FAS 131 is
effective for financial statements for years beginning after December 15, 1997.

         The Company operates in the one product line of oil and gas production
in limited geographic areas. This information and information about major
customers historically has been disclosed in the Company's annual financial
statements.



                                       15

<PAGE>   16



                           PART II - OTHER INFORMATION


ITEM 6.           EXHIBITS AND REPORTS ON FORM 8-K

EXHIBITS

     Exhibit
     Number       Description of Exhibit
     -------      ----------------------

     *10.24       First Amendment to Amended and Restated Credit Agreement dated
                  as of December 30, 1997 between Bankers Trust Company, as
                  Agent and Union Bank of California, N.A., as Co-Agent and the
                  Company

     *10.25       Second Amendment to Amended and Restated Credit Agreement 
                  dated as of January 14, 1998 between Bankers Trust Company, as
                  Agent and Union Bank of California, N.A., as Co-Agent and the
                  Company

     *10.26       Third Amendment to Amended and Restated Credit Agreement dated
                  as of February 26, 1998 between Bankers Trust Company, as
                  Agent and Union Bank of California, N.A., as Co-Agent and the
                  Company

     *10.27       Fourth Amendment to Amended and Restated Credit Agreement 
                  dated as of March 24, 1998 between Bankers Trust Company, as
                  Agent and Union Bank of California, N.A., as Co-Agent and the
                  Company

     *27.1        Financial Data Schedule


*    Filed herewith


REPORTS ON FORM 8-K

                       None.





                                       16
<PAGE>   17





                                   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 thereunto duly authorized.


                                             COSTILLA ENERGY, INC.




Date:  May  15, 1998                          By: /s/ BOBBY W. PAGE
                                                 -------------------------------
                                                  Bobby W. Page
                                                  Senior Vice President
                                                  and Chief Financial Officer






                                       17



<PAGE>   18


                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
     Exhibit
     Number       Description of Exhibit
     -------      ----------------------

<S>               <C>
     *10.24       First Amendment to Amended and Restated Credit Agreement dated
                  as of December 30, 1997 between Bankers Trust Company, as
                  Agent and Union Bank of California, N.A., as Co-Agent and the
                  Company

     *10.25       Second Amendment to Amended and Restated Credit Agreement 
                  dated as of January 14, 1998 between Bankers Trust Company, as
                  Agent and Union Bank of California, N.A., as Co-Agent and the
                  Company

     *10.26       Third Amendment to Amended and Restated Credit Agreement dated
                  as of February 26, 1998 between Bankers Trust Company, as
                  Agent and Union Bank of California, N.A., as Co-Agent and the
                  Company

     *10.27       Fourth Amendment to Amended and Restated Credit Agreement 
                  dated as of March 24, 1998 between Bankers Trust Company, as
                  Agent and Union Bank of California, N.A., as Co-Agent and the
                  Company

     *27.1        Financial Data Schedule


*    Filed herewith
</TABLE>