<PAGE>
 
                      SECURITIES AND EXCHANGE COMMISSION

                            Washington, D. C. 20549

                                   Form 10-Q

               QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15 (d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934


For the Quarter ended
      March 31, 1997                         Commission File Number 2-71865
---------------------                        ------------------------------

                         TEXLAND DRILLING PROGRAM-1981
                         -----------------------------
                             (Name of Registrant)


        TEXAS                                           75-1791491   
-----------------------                     ------------------------------------
(State of Organization)                     (I.R.S. Employer Identification No.)


500 Throckmorton Street, Suite 3100
        Fort Worth, Texas                                         76102
-----------------------------------                             ---------
  (Address of Executive Offices)                                 Zip Code


                Registrant's Telephone Number   (817) 336-2751
                                                --------------

          Securities registered pursuant to Section 12(b) of the Act:

Units of Limited Partnership Interest                               None  
-------------------------------------                          --------------
         (Title of Class)                                      (Voting Units)


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 
        ----     ----         



                   This report contains a total of 10 pages.

                                       1
<PAGE>
 
                         TEXLAND DRILLING PROGRAM-1981

                         INDEX TO FINANCIAL STATEMENTS


                                Reference Page
                                --------------

Balance Sheets at March 31, 1997 and                              
  December 31, 1996.                                               3

Statements of Operations for the Three Months  
  Ended March 31, 1997 and 1996.                                   4

Statement of Partners' Equity at March 31, 1997.                   5
 
Statements of Cash Flows for Three Months Ended       
  March 31, 1997 and 1996.                                         6  
 
Notes to Financial Statements.                                   7-8

                                       2
<PAGE>
                        TEXLAND DRILLING PROGRAM - 1981
                             (A LIMITED PARTNERSHIP)

                                 BALANCE SHEETS
                      MARCH 31, 1997 AND DECEMBER 31, 1996
                                   (UNAUDITED)
<TABLE>
<CAPTION>
                                     ASSETS
                                                    3/31/97      12/31/96
                                                  -----------   -----------
<S>                                               <C>           <C> 
CURRENT ASSETS   
  CASH                                            $    64,324   $    92,858
  ACCOUNTS RECEIVABLE
    TRADE                                             120,347       179,111
    GENERAL PARTNER (NOTE 4)                                -             -
                                                  -----------   -----------
      TOTAL CURRENT ASSETS                            184,671       271,969

PROPERTY AND EQUIPMENT, AT COST
  (SUCCESSFUL EFFORTS METHOD)
    INTANGIBLE DEVELOPMENT COSTS                    7,774,189     7,716,701
    LEASE AND WELL EQUIPMENT                        4,497,411     4,456,082
    PRODUCING LEASEHOLDS                              373,169       372,869
                                                  -----------   -----------
                                                   12,644,769    12,545,651
    LESS ACCUMULATED DEPRECIATION AND DEPLETION     9,490,936     9,415,355
                                                  -----------   -----------
                                                    3,153,832     3,130,296
    WELLS-IN-PROGRESS
    NONPRODUCING LEASEHOLDS                                 -             -
                                                  -----------   -----------
      NET PROPERTY AND EQUIPMENT                    3,153,832     3,130,296

ORGANIZATIONAL COSTS (NET OF $1,141,028
  AMORTIZATION IN 1991 AND $1,069,798 IN 1990)              -             -
                                                  -----------   -----------
                                                  $ 3,338,504   $ 3,402,265
                                                  ===========   ===========

                         LIABILITIES AND PARTNERS' EQUITY

CURRENT LIABILITIES
  ACCOUNTS PAYABLE - TRADE                             59,062        46,594
                                                  -----------   -----------
    TOTAL CURRENT LIABILITIES                          59,062        46,594

PARTNERS' EQUITY
  LIMITED PARTNERS - 2,425 UNITS OUTSTANDING        2,339,877     2,380,316
  GENERAL PARTNER                                     939,565       975,355
                                                  -----------   -----------
    TOTAL PARTNERS' EQUITY                          3,279,442     3,355,671
                                                  -----------   -----------
  TOTAL LIABILITIES AND PARTNERS' EQUITY            3,338,504     3,402,265
                                                  ===========   ===========
</TABLE>

                             SEE ACCOMPANYING NOTES

                                       3
<PAGE>
                         TEXLAND DRILLING PROGRAM - 1981
                             (A LIMITED PARTNERSHIP)

                            STATEMENTS OF OPERATIONS
                             MARCH 31, 1997 AND 1996
                                   (UNAUDITED)
<TABLE>
<CAPTION>
                                       THREE MONTHS ENDED
                                              MARCH
                                         1997       1996
                                       --------   --------
<S>                                    <C>        <C> 
REVENUES
  OIL AND GAS SALES                    $404,620   $326,100
  INTEREST INCOME                           623        592
  GAIN ON SALE                                -          -
                                       --------   --------
                                        405,243    326,692

EXPENSES
  FEES TO MANAGING GENERAL PARTNER       19,600     16,050
  PRODUCTION EXPENSES                   135,451    112,095
  SEVERANCE TAX WITHHOLDING              18,613     15,001
  DEPRECIATION, DEPLETION AND AMORT      75,581     89,066
  OTHER EXPENSES                              -     10,800
                                       --------   --------
                                        249,245    243,012

NET INCOME (LOSS)                      $155,998   $ 83,680
                                       --------   --------

NET INCOME (LOSS) ALLOCATION
  LIMITED PARTNERS                       68,581     31,886
  GENERAL PARTNER                        86,186     51,794
                                       --------   --------
                                       $154,767   $ 83,680
                                       --------   --------
NET INCOME (LOSS) PER $5000 LIMITED
  PARTNER UNIT (2,425 UNITS O/S)       $     28   $     13
                                       --------   --------
</TABLE>


                             SEE ACCOMPANYING NOTES


                                       4
<PAGE>
                         TEXLAND DRILLING PROGRAM - 1981
                             (A LIMITED PARTNERSHIP)

                          STATEMENT OF PARTNERS' EQUITY
                        THREE MONTHS ENDED MARCH 31, 1997
                                   (UNAUDITED)
<TABLE>
<CAPTION>
                                             LIMITED        GENERAL
                               TOTAL         PARTNER        PARTNER
                            -----------    -----------    -----------
<S>                         <C>            <C>            <C> 
BALANCE DECEMBER 31, 1996   $ 3,355,671    $ 2,380,421    $   975,250

PARTNERS' CONTRIBUTIONS          41,629              0         41,629

PARTNERS' DISTRIBUTIONS        (272,625)      (109,125)      (163,500)

NET INCOME / (LOSS)             154,767         68,581         86,186
                            -----------    -----------    -----------
BALANCE MARCH 31, 1997      $ 3,279,442    $ 2,339,877    $   939,565
                            ===========    ===========    ===========
</TABLE>


                             SEE ACCOMPANYING NOTES


                                       5
<PAGE>
                       TEXLAND DRILLING PROGRAM - 1981
                             (A LIMITED PARTNERSHIP)

                            STATEMENTS OF CASH FLOWS
                   THREE MONTHS ENDED MARCH 31, 1997 AND 1996
                                   (UNAUDITED)
<TABLE>
<CAPTION>
                                                       1997         1996
                                                    ---------    ---------
<S>                                                 <C>          <C> 
CASH FLOWS FROM OPERATING ACTIVITIES:            
  NET INCOME / (LOSS)                               $ 154,767    $  83,680
  ADJUSTMENTS TO RECONCILE NET INCOME TO NET CASH
    PROVIDED BY OPERATING ACTIVITIES:
        DEPRECIATION, DEPLETION, AND AMORTIZATION      75,581       89,067
        ABANDONED LEASEHOLDS
        LOSS ON SALE OF ASSETS
        CHANGE IN ACCOUNTS RECEIVABLE                  58,764       49,981
        CHANGE IN ACCOUNTS PAYABLE                     12,468       (2,497)
                                                    ---------    ---------
       TOTAL ADJUSTMENTS                              146,813      136,551
                                                    ---------    ---------
       NET CASH PROVIDED BY OPERATING ACTIVITIES      301,580      220,231

CASH FLOWS FROM INVESTING ACTIVITIES:
  ACQUISITION OF PROPERTY AND EQUIPMENT               (99,118)     (34,080)
  PROCEEDS FROM SALE OF PROPERTY AND EQUIPMENT              -
                                                    ---------    ---------
       NET CASH USED BY INVESTING ACTIVITIES          (99,118)     (34,080)

CASH FLOWS FROM FINANCING ACTIVITIES:
  PARTNERS' CONTRIBUTIONS                              41,629       14,197
  PARTNERS' DISTRIBUTIONS                            (272,625)    (173,925)
                                                    ---------    ---------
       NET CASH USED BY FINANCING ACTIVITIES         (230,996)    (159,728)

NET INCREASE IN CASH                                  (28,534)      26,423
CASH AT BEGINING OF YEAR                               92,858       70,913
                                                    ---------    ---------
CASH AT END OF QUARTER                              $  64,324    $  97,336
                                                    =========    =========
</TABLE>

                             SEE ACCOMPANYING NOTES

                                       6
<PAGE>
 
                         TEXLAND DRILLING PROGRAM-1981

                            (A Limited Partnership)


                         NOTES TO FINANCIAL STATEMENTS
                                March 31, 1997
                                  (Unaudited)



1.  SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES


The Partnership was organized as a limited partnership on June 20, 1981 for the
purpose of engaging in oil and gas exploration and production.  Texland
Properties-1981, a general partnership, and Texland Petroleum, Inc. are the
General Partners.  The Managing General Partner is Texland Petroleum, Inc.  The
Partnership's accounting policies are summarized below:


BASIS OF ACCOUNTING - The Partnership follows generally accepted accounting
principles applicable to established enterprises in the extractive industries
under a method which is generally known as the successful method of accounting.

PROPERTY AND EQUIPMENT - Costs incurred for the acquisition of producing and
nonproducing leaseholds are capitalized.  Costs of intangible development and
lease and well equipment incurred to drill and equip successful exploratory and
development wells are capitalized.  Costs to drill and equip unsuccessful
exploratory wells are charged to operations while costs of unsuccessful
development wells remain capitalized.  Costs associated with uncompleted wells
are capitalized as wells-in-progress.

ABANDONED LEASEHOLDS - Costs of nonproducing properties are charged to expense
at such time as they are deemed to be impaired, based upon periodic assessments
of such costs.

DEPLETION - Leasehold costs of producing properties are amortized on the unit of
production method based on proved oil and gas reserves.  Intangible development
costs of producing properties are amortized on the unit of production method
based on estimated proved developed oil and gas reserves.

DEPRECIATION - Depreciation of equipment is provided by using the unit of
production method based on estimated proved developed oil and gas reserves.

ORGANIZATION COSTS - These costs are amortized by the straight-line method over
ten years, the life of the Partnership.

FEDERAL INCOME TAX - The Partnership files its federal income tax return on the
accrual basis.

                                       7
<PAGE>
 
                         TEXLAND DRILLING PROGRAM-1981

                            (A Limited Partnership)


                   NOTES TO FINANCIAL STATEMENTS (Continued)
                                 March 31, 1997
                                  (Unaudited)



2.  CONTRIBUTIONS BY GENERAL PARTNER (TEXLAND PROPERTIES-1981)


Under terms of the Partnership Agreement, the General Partner is charged for
certain costs related to drilling and production operations which are required
to be capitalized for federal income tax purposes.  These costs are treated as
capital contributions by the General Partner.  In addition, Texland Properties-
1981 and Texland Petroleum, Inc. have invested in limited partnership units in
the amount of $95,000 and $30,000 respectively.



3.  FEES TO MANAGING GENERAL PARTNER (TEXLAND PETROLEUM, INC.)


In consideration of its management services rendered, the Managing General
Partner is entitled to charge management fees to the Partnership.  In addition,
for the three months ended March 31, 1997  and March 31, 1996, the Partnership
was charged $36,812 and $35,745 respectively for technical services, accounting
services, and supervisory services performed by the employees of the Managing
General Partner and such charges are included in intangible development costs,
production expenses and fees to Managing General Partner.  These charges are
allocated between the General and Limited Partners based upon applicable revenue
and expense sharing rates.

                                       8
<PAGE>
 
                         TEXLAND DRILLING PROGRAM-1981

                            (A Limited Partnership)


               MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                      CONDITION AND RESULTS OF OPERATIONS

                                March 31, 1997



The Partnership's average price per barrel of oil for the first quarter of 1997
was $18.44 as compared to $15.65 for the first quarter of 1996. The increased
revenue results primarily from the increase in average oil prices and increased
production due to in-fill drilling in 1996 on certain Partnership properties.


Expenses were comparable for the 1997 and 1996 three month period.  Although
sales amounts increased, volume sales were not sufficiently impacted to
materially affect operating expense levels.

The Partnership was formed with cash contributions from the Limited and General
Partners.  Management does not intend to incur any substantial indebtedness and
any developmental drilling which is necessary will be processed by farmout to
other parties or by reinvestment of internally generated funds.  Management,
therefore, anticipates no liquidity problems during the life of the Partnership.

                                       9
<PAGE>
 
PART II



Items 1 through 6
-----------------

Omitted - Not applicable to Registrant.



                                   SIGNATURE
                                   ---------



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


                                   TEXLAND DRILLING PROGRAM-1981



                                   By    /s/  M. E. Chapman        
                                         -----------------------------
                                         M. E. Chapman, Vice President
                                         of Texland Petroleum, Inc.,
                                         General Partner - Texland
                                         Properties-1981



Date: August 1, 1997

                                       10