<PAGE>   1
  
                                                                    EXHIBIT 99.1
 
                             LETTER OF TRANSMITTAL
 
              TO TENDER UNREGISTERED 10 1/4% SENIOR NOTES DUE 2006
 
                                       OF
 
                             COSTILLA ENERGY, INC.
 
                PURSUANT TO THE OFFER TO EXCHANGE AND PROSPECTUS
 
                          DATED                , 1998
 
                             ---------------------
 
THE EXCHANGE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 5:00 P.M., NEW YORK CITY
 TIME, ON [          ], 1998 (THE "EXPIRATION DATE"), UNLESS THE EXCHANGE OFFER
                           IS EXTENDED BY THE COMPANY
 
                             ---------------------
 
             PLEASE FOLLOW CAREFULLY THE ACCOMPANYING INSTRUCTIONS
 
                                 EXCHANGE AGENT
 
Send this Letter of Transmittal and certificate(s) representing unregistered
10 1/4% Senior Notes due 2006 (the "Private Notes") of Costilla Energy, Inc. to
STATE STREET BANK AND TRUST COMPANY, the Exchange Agent for the Exchange Offer,
as follows:
 
<TABLE>
<S>                                                 <C>
         By Registered or Certified Mail,
         Overnight Mail or Hand Delivery:                              By Facsimile:
        STATE STREET BANK AND TRUST COMPANY                 STATE STREET BANK AND TRUST COMPANY
            CORPORATE TRUST DEPARTMENT                     ATTENTION: CORPORATE TRUST DEPARTMENT
              TWO INTERNATIONAL PLACE                                 (617) 664-5371
            BOSTON, MASSACHUSETTS 02110
</TABLE>
 
  Delivery of this Letter of Transmittal to an address other than as set forth
 above will not constitute a valid delivery (originals of all documents sent by
  facsimile should be sent promptly by registered or certified mail, overnight
                            mail or hand delivery).
 
                               INFORMATION AGENT
 
     For information concerning the Exchange Offer, contact D. F. KING & CO.
INC., the Information Agent for the Exchange Offer, as follows:
 
<TABLE>
<S>                                                 <C>
           By Registered Certified Mail,
         Overnight Mail or Hand Delivery:                              By Telephone:
               D.F. KING & CO., INC.                               D.F. KING & CO., INC.
                  77 WATER STREET                                     (800) 207-2872
             NEW YORK, NEW YORK 10005
</TABLE>
 
   IF YOU WISH TO EXCHANGE PRIVATE NOTE(S) FOR AN EQUAL AMOUNT OF REGISTERED
 10 1/4% SENIOR NOTES DUE 2006 (THE "EXCHANGE NOTES") PURSUANT TO THE EXCHANGE
OFFER, YOU MUST VALIDLY TENDER (AND NOT WITHDRAW) PRIVATE NOTES TO THE EXCHANGE
                      AGENT PRIOR TO THE EXPIRATION DATE.
 
<TABLE>
<S>                                                          <C>                     <C>
---------------------------------------------------------------------------------------------------------
                                      DESCRIPTION OF NOTES TENDERED
---------------------------------------------------------------------------------------------------------
      NAME(S) AND ADDRESS(ES) OF REGISTERED HOLDER(S)
 (PLEASE FILL IN. IF ALREADY FILLED IN, PLEASE CORRECT ANY
                          ERRORS.)                           COSTILLA ENERGY, INC. PRIVATE NOTES TENDERED
---------------------------------------------------------------------------------------------------------
                                                                                     AGGREGATE PRINCIPAL
                                                                   CERTIFICATE        AMOUNT OF PRIVATE
                                                                    NUMBER(S)           NOTES TENDERED
                                                             ------------------------------------------
 
                                                             ------------------------------------------
 
                                                             ------------------------------------------
 
                                                             ------------------------------------------
                                                             Total Amount
---------------------------------------------------------------------------------------------------------
</TABLE>
 
               (ATTACH A SEPARATE, SIGNED SCHEDULE IF NECESSARY)
<PAGE>   2
 
                              TERMS AND CONDITIONS
 
     1. The undersigned hereby tenders to Costilla Energy, Inc., a Delaware
corporation (the "Company"), the Private Notes described above pursuant to the
Company's offer of $1,000 principal amount of registered Exchange Notes in
exchange for $1,000 principal amount of the Private Notes, upon the terms and
subject to the conditions contained in the Prospectus dated             , 1998
(the "Prospectus"), receipt of which is hereby acknowledged, and in this Letter
of Transmittal (which together constitute the "Exchange Offer").
 
     2. The undersigned hereby represents and warrants that it has full power
and authority to tender the Private Notes described above and that the Company
will acquire good and unencumbered title thereto, free and clear of all liens,
restrictions, charges and encumbrances and not subject to any adverse claim. The
undersigned will, upon request, execute and deliver any additional documents
deemed by the Company to be necessary or desirable to complete the tender of the
Private Notes.
 
     3. The undersigned understands that the tender of the Private Notes
pursuant to all of the procedures set forth in the Prospectus and this Letter of
Transmittal will constitute an agreement between the undersigned and the Company
as to the terms and conditions set forth in the Prospectus and this Letter of
Transmittal.
 
     4. The undersigned hereby represents and warrants that:
 
          (a) the Exchange Notes acquired by it pursuant to the Exchange Offer
     are being obtained in the ordinary course of business of the undersigned,
     whether or not the undersigned is the holder;
 
          (b) neither the undersigned nor any such other person is engaging in
     or intends to engage in a distribution of the Exchange Notes;
 
          (c) neither the undersigned nor any such other person has an
     arrangement or understanding with any person to participate in the
     distribution (within the meaning of the Securities Act of 1933, as amended
     (the "Securities Act")), of such Exchange Notes; and
 
          (d) neither the holder nor any such other person is an "affiliate," as
     such term is defined under Rule 405 promulgated under the Securities Act,
     of the Company.
 
     5. If the undersigned is not a broker-dealer, the undersigned represents
that it is not engaged in, and does not intend to engage in, a distribution of
Exchange Notes. If the undersigned is a broker-dealer, the undersigned
represents that it acquired the Private Notes for its own account as a result of
market-making activities or other trading activities. If the undersigned is a
broker-dealer that will receive Exchange Notes for its own account in exchange
for Private Notes that were acquired as a result of market-making activities or
other trading activities, it acknowledges that it will deliver a prospectus in
connection with any resale of such Exchange Notes; however, by so acknowledging
and by delivering a prospectus, the undersigned will not be deemed to admit that
it is an "underwriter" within the meaning of the Securities Act. If the
undersigned is a broker-dealer and the Private Notes held for its account were
not acquired as a result of market-making or other trading activities, such
Private Notes cannot be exchanged pursuant to the Exchange Offer.
 
     6. Any obligation of the undersigned hereunder shall be binding upon the
successors, assigns, executors, administrators, trustees in bankruptcy and legal
and personal representatives of the undersigned.
 
     7. This tender is irrevocable, subject to withdrawal rights described in
the Prospectus.
 
     8. Unless otherwise indicated herein under "Special Delivery Instructions,"
please issue the Exchange Notes in the name of the undersigned.
<PAGE>   3
 
                         SPECIAL DELIVERY INSTRUCTIONS
                              (SEE INSTRUCTION 1)
 
     To be completed ONLY IF the Exchange Notes are to be issued or sent to
someone other than the undersigned or to the undersigned at an address other
than provided above.
 
     Mail  [ ]     Issue  [ ]  (check appropriate boxes) Exchange Notes to:
 
                                            Name:
                                               ---------------------------------
                                                        (PLEASE PRINT)
 
                                            Address:
                                                --------------------------------
 
                                                --------------------------------
 
                                                --------------------------------
                                                      (INCLUDING ZIP CODE)
 
                                   SIGNATURE
 
     To be completed by all exchanging noteholders. Must be signed by the
registered holder exactly as its name appears of record for the Private Notes.
If signature is by trustee, executor, administrator, guardian, attorney-in-fact,
officer of a corporation or other person acting in a fiduciary or representative
capacity, please set forth full title. See Instruction 3.
 
                                            X
                                             -----------------------------------
 
                                            X
                                             -----------------------------------
                                                 SIGNATURE(S) OF REGISTERED
                                              HOLDER(S) OR AUTHORIZED SIGNATURE
 
                                            Dated:
                                               ---------------------------------
 
                                            Name(s):
                                                 -------------------------------
 
                                                 -------------------------------
                                                     (PLEASE TYPE OR PRINT)
 
                                            Capacity:
                                                 -------------------------------
 
                                            Address:
                                                --------------------------------
 
                                                --------------------------------
 
                                                --------------------------------
                                                      (INCLUDING ZIP CODE)
 
                                            Area Code and Telephone No.:
 
                                            ------------------------------------
<PAGE>   4
 
               SIGNATURE GUARANTEE (IF REQUIRED BY INSTRUCTION 1)
 
     Certain Signatures Must Be Guaranteed by an Eligible Institution
 
         --------------------------------------------------------------
             (NAME OF ELIGIBLE INSTITUTION GUARANTEEING SIGNATURES)
 
         --------------------------------------------------------------
               (ADDRESS (INCLUDING ZIP CODE) AND TELEPHONE NUMBER
                         (INCLUDING AREA CODE) OF FIRM)
 
         --------------------------------------------------------------
                             (AUTHORIZED SIGNATURE)
 
         --------------------------------------------------------------
                                 (PRINTED NAME)
 
         --------------------------------------------------------------
                                    (TITLE)
 
Dated:
         --------------------------------------------------------------
 
              PLEASE READ THE INSTRUCTIONS ON THE FOLLOWING PAGE,
                WHICH FORM A PART OF THIS LETTER OF TRANSMITTAL.
<PAGE>   5
 
                     INSTRUCTIONS TO LETTER OF TRANSMITTAL
 
     1. GUARANTEE OF SIGNATURES. Unless the box titled "Special Delivery
Instructions" above has not been completed or the Private Notes described above
are tendered for the account of an Eligible Institution (as defined) signatures
on this Letter of Transmittal must be guaranteed by an eligible guarantor
institution that is a member of or participant in the Securities Transfer Agents
Medallion Program, the New York Stock Exchange Medallion Signature Program, the
Stock Exchange Medallion Program, or an "eligible guarantor institution" within
the meaning of Rule 17Ad-15 promulgated under the Securities Exchange Act of
1934, as amended (an "Eligible Institution").
 
     2. DELIVERY OF LETTER OF TRANSMITTAL AND PRIVATE NOTES. Private Notes
together with a properly completed and duly executed Letter of Transmittal (or
copy thereof), should be mailed or delivered to the Exchange Agent at the
address set forth above.
 
     THE METHOD OF DELIVERY OF PRIVATE NOTES AND THE LETTER OF TRANSMITTAL AND
ALL OTHER REQUIRED DOCUMENTS TO THE EXCHANGE AGENT IS AT THE ELECTION AND RISK
OF THE HOLDER. INSTEAD OF DELIVERY BY MAIL, IT IS RECOMMENDED THAT HOLDERS USE
AN OVERNIGHT OR HAND DELIVERY SERVICE. IN ALL CASES, SUFFICIENT TIME SHOULD BE
ALLOWED TO ASSURE DELIVERY TO THE EXCHANGE AGENT BEFORE THE EXPIRATION DATE. NO
LETTER OF TRANSMITTAL OR PRIVATE NOTES SHOULD BE SENT TO THE COMPANY. HOLDERS
MAY REQUEST THEIR RESPECTIVE BROKERS, DEALERS, COMMERCIAL BANKS, TRUST
COMPANIES, OR NOMINEES TO EFFECT THE ABOVE TRANSACTIONS FOR SUCH HOLDERS.
 
     3. SIGNATURE ON LETTER OF TRANSMITTAL, BOND POWERS AND ENDORSEMENTS. If
this Letter of Transmittal is signed by a person other than a registered holder
of Private Notes, such Private Notes must be accompanied by appropriate bond
powers, signed by such registered holder exactly as such registered holder's
name appears on such Private Notes.
 
     If this Letter of Transmittal or any Private Notes or bond powers are
signed by trustees, executors, administrators, guardians, attorneys-in-fact,
officers of corporations, or others acting in a fiduciary or representative
capacity, such persons should so indicate when signing, and, unless waived by
the Company, proper evidence satisfactory to the Company of their authority to
so act must be submitted with this Letter of Transmittal.
 
     4. TAX INFORMATION. Please complete the attached Substitute Form W-9. See
"Tax Information and Guidelines."
 
     5. MISCELLANEOUS. All questions as to the validity, form, eligibility
(including time of receipt), acceptance, and withdrawal of tendered Private
Notes will be resolved by the Company in its sole discretion, which
determination will be final and binding. The Company reserves the absolute right
to reject any or all Private Notes not properly tendered or any Private Notes
the Company's acceptance of which would, in the opinion of counsel for the
Company, be unlawful. The Company also reserves the right to waive any defects,
irregularities, or conditions of tender as to particular Private Notes. The
Company's interpretation of the terms and conditions of the Exchange Offer
(including the instructions in this Letter of Transmittal) will be final and
binding. Unless waived, any defects or irregularities in connection with tenders
of Private Notes must be cured within such time as the Company shall determine.
Neither the Company, the Exchange Agent, nor any other person shall be under any
duty to give notification of defects in such tenders nor shall any such person
incur any liability for failure to give such notification. Tenders of Private
Notes will not be deemed to have been made until such defects or irregularities
have been cured or waived. Any Private Notes received by the Exchange Agent that
are not properly tendered and as to which the defects or irregularities have not
been cured or waived will be returned by the Exchange Agent to the tendering
holder thereof as soon as practicable following the Expiration Date.
<PAGE>   6
 
                         TAX INFORMATION AND GUIDELINES
 
     You must provide the Exchange Agent with your correct Taxpayer
Identification Number ("TIN") on the Substitute Form W-9 set forth below. If you
are an individual, your TIN is your social security number.
 
     On the Substitute Form W-9, you must certify under penalties of perjury
that: (a) your TIN is correct, and (b) you are not subject to backup
withholding, either because the Internal Revenue Service ("IRS") has not
notified you that you are subject to backup withholding as a result of a failure
to report interest or dividends or because the IRS has notified you that you are
no longer subject to backup withholding. If the IRS has notified you that you
are subject to backup withholding because of underreporting of interest or
dividends, you must cross out item (2) in the "Certification" section of the
Substitute Form W-9. If subsequently, however, the IRS notifies you that you are
not longer subject to backup withholding, you should not cross out item (2).
 
     Exempt persons, which include all corporations and certain foreign
individuals, are not subject to the backup withholding and reporting
requirements. An exempt person should furnish its TIN, write "Exempt" on the
face of the Substitute Form W-9, and sign and date the form. To satisfy the
Exchange Agent that a foreign person qualifies as an exempt recipient, such
person must also submit to the Exchange Agent with this Letter of Transmittal a
Form W-8, Certificate of Foreign Status, signed under penalties of perjury,
attesting to such person's foreign status.
 
     If you are required to provide a TIN, but have not been issued a TIN and
have applied for one, or intend to apply for one in the near future, you should
write "Applied For" on the line of the Substitute Form W-9 requiring a TIN.
Generally, you will then have 60 days to get a TIN and give it to the Exchange
Agent. If the Exchange Agent does not receive your TIN within 60 days, backup
withholding, if applicable, will begin.
 
     If you do not provide the Exchange Agent with your correct TIN, you may be
subject to a $50 penalty that the IRS imposes. Failure to comply truthfully with
the backup withholding certification requirements may also result in the
imposition of criminal and civil fines and penalties.
<PAGE>   7
 
<TABLE>
<S>                                <C>                                                       <C>
----------------------------------------------------------------------------------------------------------------------------------
 Name, as shown on first page hereof (if held in joint account, list first and circle the name of the person or entity whose
 number you enter in Part I below.)
 
 ---------------------------------------------------------------------------------------------------------------------------------
 Address (if not completed, signature in Part 1 below will constitute a certification that the address on the first page hereof is
 correct.)
 
 ---------------------------------------------------------------------------------------------------------------------------------
 City, State and ZIP code
 
 ---------------------------------------------------------------------------------------------------------------------------------
 SUBSTITUTE                         PART I -- PLEASE PROVIDE YOUR TIN IN THE BOX AT RIGHT      TIN -----------------------------
 FORM W-9                           AND CERTIFY BY SIGNING AND DATING BELOW.                       Social Security Number or
                                                                                                Employer Identification Number
                                    ----------------------------------------------------------------------------------------------
 DEPARTMENT OF THE TREASURY         PART II -- Awaiting TIN [ ]
 INTERNAL REVENUE SERVICE           For Payees exempt from backup withholding, see the enclosed Guidelines for Certification of
 PAYOR'S REQUEST FOR TAXPAYER       Taxpayer Number on Substitute Form W-9 and complete as instructed under "Important Tax
 IDENTIFICATION NUMBER (TIN)        Information" above.
</TABLE>
 
--------------------------------------------------------------------------------
 CERTIFICATION. Under penalties of perjury, I certify that:
 (1) The number shown on this form is my correct Taxpayer Identification Number
     (or I am waiting for a number to be issued to me), and
 (2) I am not subject to backup withholding either because I have not been
     notified by the Internal Revenue Service ("IRS") that I am subject to
     backup withholding as a result of a failure to report all interest or
     dividends, or the IRS has notified me that I am no longer subject to
     backup withholding.
 
 CERTIFICATION INSTRUCTIONS. You must cross out item (2) above if you have been
 notified by the IRS that you are subject to backup withholding because of
 under reporting interest or dividends on your tax return. However, if after
 being notified by the IRS that you were subject to backup withholding you
 received any other notification from the IRS that you are no longer subject to
 backup withholding, do not cross out item (2). (Also see the enclosed
 Guidelines for Certification of Taxpayer Identification Number on Substitute
 Form W-9.)
 
SIGNATURE:                                DATE:
          -------------------------------       --------------------------------
<PAGE>   8
 
            GUIDELINES FOR CERTIFICATION OF TAXPAYER IDENTIFICATION
                         NUMBER OF SUBSTITUTE FORM W-9
 
GUIDELINES FOR DETERMINING THE PROPER IDENTIFICATION NUMBER TO GIVE THE
PAYER. -- Social Security numbers have nine digits separated by two hyphens:
i.e. 000-00-0000. Employer identification numbers have nine digits separated by
only one hyphen: i.e. 00-0000000. The table below will help determine the number
to give the payer.
 
<TABLE>
<C>  <S>                           <C>
---------------------------------------------------------
        FOR THIS TYPE OF ACCOUNT:  GIVE THE
                                   SOCIAL SECURITY
                                   NUMBER OF --
---------------------------------------------------------
 1.  An individual's account       The individual
 2.  Two or more individuals       The actual owner of
     (joint account)               the account or, if
                                   combined funds, any
                                   one of the
                                   individuals(1)
 3.  Husband and wife (joint       The actual owner of
     account)                      the account or, if
                                   joint funds, either
                                   person(1)
 4.  Custodian account of a minor  The minor(2)
     (Uniform Gift to Minors Act)
 5.  Adult and minor (joint        The adult or, if the
     account)                      minor is the only
                                   contributor, the
                                   minor(1)
 6.  Account in the name of        The ward, minor, or
     guardian or committee for a   incompetent person(3)
     designated ward, minor, or
     incompetent person
 7.  a. The usual revocable        The grantor-
        savings trust account      trustee(1)
        (grantor is also trustee)
     b. So-called trust account    The actual owner(1)
        that is not a legal or
        valid trust under State
        law.
=========================================================
        FOR THIS TYPE OF ACCOUNT:  GIVE THE
                                   EMPLOYER
                                   IDENTIFICATION
                                   NUMBER OF --
---------------------------------------------------------
 8.  Sole proprietorship account.  The owner
 9.  A valid trust, estate, or     The legal entity (do
     pension trust.                not furnish the
                                   identifying number of
                                   the personal
                                   representative or
                                   trustee unless the
                                   legal entity itself is
                                   not designated in the
                                   account title.)(5)
10.  Corporate account             The corporation
11.  Religious, charitable, or     The organization
     educational organization
     account.
12.  Partnership account held in   The partnership
     the name of the business.
13.  Association, club, or other   The organization
     tax-exempt organization.
14.  A broker or registered        The broker or nominee
     nominee
15.  Account with the Department   The public entity
     of Agriculture in the name
     of a public entity (such as
     a State or local government,
     school district, or prison)
     that receives agricultural
     program payments
---------------------------------------------------------
</TABLE>
 
(1) List first and circle the name of the person whose number you furnish.
(2) Circle the minor's name and furnish the minor's social security number.
(3) Circle the ward's, minor's or incompetent person's name and furnish such
    person's social security number.
(4) Show the name of the owner.
(5) List first and circle the name of the legal trust, estate, or pension trust.
 
NOTE:If no name is circled when there is more than one name, the number will be
     considered to be that of the first name listed.