<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                             
 September 30, 1996                               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 September 30, 1996 and  
  December 31, 1995                                                          3

Statements of Operations for the Three Months  
  Ended September 30, 1996 and 1995 and the Nine
  Months Ended September 30, 1996 and 1995.                                  4

Statement of Partners' Equity at September 30, 1996                          5
 
Statements of Cash Flows for Nine Months Ended           
  September 30, 1996 and 1995                                                6
 
Notes to Financial Statements                                              7-8

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

                                BALANCE SHEETS
                   SEPTEMBER 30, 1996 AND DECEMBER 31, 1995
                                  (UNAUDITED)

                                    ASSETS
<TABLE>
<CAPTION>                                                               
                                                    9/30/96       12/31/95
                                                 -----------   ----------- 
<S>                                                 <C>           <C> 
CURRENT ASSETS
  CASH                                           $   103,895   $    70,913
  ACCOUNTS RECEIVABLE                                
    TRADE                                            140,167       165,044
    GENERAL PARTNER (NOTE 4)                               -             -
                                                 -----------   -----------
      TOTAL CURRENT ASSETS                           244,062       235,957
                                                 
PROPERTY AND EQUIPMENT, AT COST                  
  (SUCCESSFUL EFFORTS METHOD)                    
    INTANGIBLE DEVELOPMENT COSTS                   7,697,928     7,598,675
    LEASE AND WELL EQUIPMENT                       4,441,287     4,384,516
    PRODUCING LEASEHOLDS                             372,294       372,066
                                                 -----------   -----------
                                                  12,511,509    12,355,257
    LESS ACCUMULATED DEPRECIATION AND DEPLETION    9,344,741     9,077,541
                                                 -----------   -----------
                                                   3,166,768     3,277,716
    WELLS-IN-PROGRESS                            
    NONPRODUCING LEASEHOLDS                                -             -
                                                 -----------   -----------
      NET PROPERTY AND EQUIPMENT                   3,166,768     3,277,716
                                                 
ORGANIZATIONAL COSTS (NET OF $1,141,028          
  AMORTIZATION IN 1991 AND 1,069,798 IN 1990)              -             -
                                                 -----------   -----------
                                                 $ 3,410,830   $ 3,513,673
                                                 ===========   ===========
                                                 
                 LIABILITIES AND PARTNERS' EQUITY             
                                                 
CURRENT LIABILITIES                              
  ACCOUNTS PAYABLE - TRADE                            63,619        64,086
                                                 -----------   -----------
    TOTAL CURRENT LIABILITIES                         63,619        64,086
                                                 
PARTNERS' EQUITY                                 
  LIMITED PARTNERS - 2,425 UNITS OUTSTANDING       2,372,118     2,442,101
  GENERAL PARTNER                                    975,093     1,007,486
                                                 -----------   -----------
    TOTAL PARTNERS' EQUITY                         3,347,211     3,449,587
                                                 -----------   -----------
  TOTAL LIABILITIES AND PARTNERS' EQUITY           3,410,830     3,513,673
                                                 ===========   ===========
</TABLE>
                            SEE ACCOMPANYING NOTES

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

                           STATEMENTS OF OPERATIONS
                          SEPTEMBER 30, 1996 AND 1995
                                  (UNAUDITED)
<TABLE>
<CAPTION>
                                   THREE MONTHS ENDED       NINE MONTHS ENDED
                                       SEPTEMBER                SEPTEMBER       
                                    1996        1995         1996        1995
                                  --------    --------    ----------    --------
<S>                               <C>         <C>         <C>           <C> 
REVENUES                        
  OIL AND GAS SALES               $441,758    $270,382    $1,168,840    $841,890
  INTEREST INCOME                      893         695         2,210       1,706
  GAIN ON SALE                           -           -             -           -
                                  --------    --------    ----------    --------
                                   442,652     271,077     1,171,050     843,596
                                
EXPENSES                        
  FEES TO MANAGING GENERAL      
   PARTNER                          16,050      16,050        48,150      48,150
  PRODUCTION EXPENSES              112,264     108,537       330,680     323,321
  SEVERANCE TAX WITHHOLDING         21,859      12,451        55,305      38,727
  DEPRECIATION, DEPLETION           
   AND AMORTIZATION                 89,066      88,830       267,199     266,489
  OTHER EXPENSES                    (6,947)     11,449        14,378      12,339
                                  --------    --------    ----------    --------
                                   232,292     237,317       715,712     689,026
                                  --------    --------    ----------    --------
NET INCOME (LOSS)                 $210,359    $ 33,760    $  455,338    $154,570
                                  --------    --------    ----------    --------
                                
NET INCOME (LOSS) ALLOCATION    
  LIMITED PARTNERS                 105,336       5,553       208,892      54,433
  GENERAL PARTNER                  105,024      28,207       246,445     100,137
                                  --------    --------    ----------    --------
                                  $210,359    $ 33,760    $  455,338    $154,570
                                  --------    --------    ----------    --------
NET INCOME (LOSS) PER $5000     
 LIMITED PARTNER UNIT           
 (2,425 UNITS O/S)                $     43    $      2    $       86    $     22
                                  --------    --------    ----------    --------
</TABLE>
                            SEE ACCOMPANYING NOTES

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

                         STATEMENT OF PARTNERS' EQUITY
                     NINE MONTHS ENDED SEPTEMBER 30, 1996
                                  (UNAUDITED)
<TABLE>
<CAPTION>
                                                  LIMITED           GENERAL
                                 TOTAL            PARTNER           PARTNER
                               ----------        ----------        ----------
<S>                            <C>               <C>               <C>
                           
BALANCE DECEMBER 31, 1995      $3,449,587        $2,442,101        $1,007,486
                           
PARTNERS' CONTRIBUTIONS            55,962                              55,962
                           
PARTNERS' DISTRIBUTIONS          (613,675)         (278,875)         (334,800)
                           
NET INCOME / (LOSS)               455,338           208,892           246,445
                               ----------        ----------        ----------
BALANCE SEPTEMBER 30, 1996     $3,347,211        $2,372,118        $  975,093
                               ==========        ==========        ==========
</TABLE>
                            SEE ACCOMPANYING NOTES

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

                           STATEMENTS OF CASH FLOWS
                 NINE MONTHS ENDED SEPTEMBER 30, 1996 AND 1995
                                  (UNAUDITED)
<TABLE>
<CAPTION>
                                                       1996            1995
                                                     ---------       ---------
<S>                                                  <C>             <C>
CASH FLOWS FROM OPERATING ACTIVITIES:              
  NET INCOME / (LOSS)                                $ 455,338       $ 154,570
  ADJUSTMENTS TO RECONCILE NET INCOME TO NET CASH  
    PROVIDED BY OPERATING ACTIVITIES:              
        DEPRECIATION, DEPLETION, AND AMORTIZATION      267,200         266,489
        ABANDONED LEASEHOLDS                       
        LOSS ON SALE OF ASSETS                     
        CHANGE IN ACCOUNTS RECEIVABLE                   24,877          23,693
        CHANGE IN ACCOUNTS PAYABLE                        (467)        (11,078)
                                                     ---------       ---------
       TOTAL ADJUSTMENTS                               291,610         279,104
                                                     ---------       ---------
       NET CASH PROVIDED BY OPERATING ACTIVITIES       746,947         433,674
                                                   
CASH FLOWS FROM INVESTING ACTIVITIES:              
  ACQUISITION OF PROPERTY AND EQUIPMENT               (156,252)        (56,253)
  PROCEEDS FROM SALE OF PROPERTY AND EQUIPMENT               -
                                                     ---------       ---------
       NET CASH USED BY INVESTING ACTIVITIES          (156,252)        (56,253)
                                                   
CASH FLOWS FROM FINANCING ACTIVITIES:              
  PARTNERS' CONTRIBUTIONS                               55,962          31,360
  PARTNERS' DISTRIBUTIONS                             (613,675)       (385,850)
                                                     ---------       ---------
       NET CASH USED BY FINANCING ACTIVITIES          (557,713)       (354,490)
                                                   
NET INCREASE IN CASH                                    32,982          22,931
CASH AT BEGINNING OF YEAR                               70,913          44,753
                                                     ---------       ---------
CASH AT END OF QUARTER                               $ 103,895       $  67,684
                                                     =========       =========
</TABLE>
                            SEE ACCOMPANYING NOTES

                                       6
<PAGE>
 
                         TEXLAND DRILLING PROGRAM-1981
                            (A Limited Partnership)

                         NOTES TO FINANCIAL STATEMENTS
                              September 30, 1996
                                  (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)
                              September 30, 1996
                                  (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 September 30, 1996  and September 30, 1995, the
Partnership was charged $35,745 and $45,055 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

                              September 30, 1996


The Partnership's average price per barrel of oil for the third quarter of 1996
was $18.39 as compared to $13.73 for the third quarter of 1995. The increased
revenue results primarily from this increase in average oil prices and increased
production due to in-fill drilling in 1995 on certain Partnership properties.

Expenses were comparable for the 1996 and 1995 three and nine month periods.
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: November 11, 1996

                                       10