<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, 1999                        Commission File Number 2-71865
-------------------                      ------------------------------

                      TEXLAND DRILLING PROGRAM-1981, LTD.
                      -----------------------------------
                             (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, LTD.
                                        
                         INDEX TO FINANCIAL STATEMENTS
                                        

                                Reference Page
                                --------------
 
Balance Sheets at March 31, 1999 and                     3
    December 31, 1998.
 
Statements of Operations for the Three Months            4
    Ended March 31, 1999 and 1998.
 
Statement of Partners' Equity at March 31, 1999.         5
 
Statements of Cash Flows for Three Months Ended          6
    March 31, 1999 and 1998.
 
Notes to Financial Statements.                         7-8

                                       2
<PAGE>
 
                     Texland Drilling Program - 1981, Ltd.
                            (A Limited partnership)

                                Balance Sheets
                     March 31, 1999 and December 31, 1998
                                  (Unaudited)
<TABLE> 
<CAPTION> 
ASSETS
                                                                                 3/31/99          12/31/98
                                                                           ---------------      ------------  
<S>                                                                        <C>                  <C> 
Current Assets
  Cash                                                                     $     20,214         $    8,308
  Accounts Receivable
    Trade                                                                        73,081             73,153
    General Partner                                                                   -                  -
                                                                          -------------        -----------
    Total Current Assets                                                         93,295             81,461
Property and Equipment, at Cost
  (Successful Efforts Method)
  Intangible Development Costs                                                7,119,641          7,119,641
  Lease and Well Equipment                                                    4,179,376          4,177,316
  Producing Leaseholds                                                          165,314            165,295
                                                                           ------------        -----------
                                                                             11,464,331         11,462,252
  Less: Accumulated Depreciation, Depletion & Amortization                    9,906,860          9,826,816
                                                                           ------------        ----------- 
                                                                              1,557,471          1,635,436
  Wells-in-Progress
  Nonproducing Leaseholds                                                             -                  -
                                                                           ------------        -----------
    Net Property, Plant and Equipment                                         1,557,471          1,635,436
Organizational Costs (net of $1,141,028 amortization in 1991
  and $1,069,798 in 1990)                                                             -                  -
                                                                           ------------        -----------
  Total Assets                                                             $  1,650,766         $1,716,897
                                                                           ============        ===========

LIABILITIES AND PARTNERS' EQUITY
Current Liabilities
  Accounts Payable - Trade                                                       40,628             43,557
                                                                           ------------        -----------
  Total Current Liabilities                                                      40,628             43,557
Partners' Equity
    Limited Partners - 2,425 Units Outstanding                                2,134,756          2,122,689
    General Partner                                                            (524,618)          (449,349)
                                                                           ------------        -----------
    Total Partners' Equity                                                    1,610,138          1,673,340
                                                                           ------------        -----------
    Total Liabilities and Partners' Equity                                    1,650,766          1,716,897
                                                                           ============        ===========
</TABLE> 

                            See Accompanying Notes

                                       3
<PAGE>
 
                     Texland Drilling Program - 1981, Ltd.
                            (A Limited Partnership)

                            Statement of Operations
                            March 31, 1999 and 1998
                                  (Unaudited)

<TABLE> 
<CAPTION> 
                                                         Three Months Ended
                                                              March 31,
                                                             1999           1998
                                                        ---------      ---------
<S>                                                     <C>            <C> 
Revenues
    Oil and Gas Sales                                   $ 171,620      $ 265,746
    Interest Income                                            94            439
    Gain on Sale                                                -              -
                                                        ---------      ---------
                                                          171,714        266,185

Expenses
    Fees to Managing General Partner                       21,975         24,260
    Production Expenses                                   100,241        123,326
    Severance Tax Withholding                               7,895         12,224
    Depreciation, Depletion & Amortization Expenses        80,044         78,905
    Other Expenses                                          1,279          1,691
                                                        ---------      ---------
                                                          211,433        240,406
                                                        ---------      ---------
Net Income (Loss)                                       $ (39,718)     $  25,779
                                                        ---------      ---------
Net Income (Loss) Allocation
    Limited Partners                                      (27,095)         5,636
    General Partner                                       (12,623)        20,114
                                                        ---------      ---------
                                                        $ (39,718)     $  25,750
                                                        ---------      ---------
Net Income (Loss) per $5,000 Limited Partner Unit        
    (2,425 Units Outstanding)                           $     (11)     $       2
                                                        ---------      ---------
</TABLE> 

                            See Accompanying Notes

                                       4
<PAGE>

                     Texland Drilling Program - 1981, Ltd.
                            (A Limited Partnership)

                         Statement of Partners' Equity
                       Three Months Ended March 31, 1999
                                  (Unaudited)

<TABLE> 
<CAPTION>                                                                        
                                                                                     
                                                                            Limited                    General 
                                                   Total                    Partner                    Partner
                                             ------------------       ------------------          ----------------    
<S>                                          <C>                      <C>                         <C>                 
Balance December 31, 1998                    $     1,673,340          $     2,122,689             $    (449,349)      
                                                                                                                      
Partners' Contributions                                2,079                                              2,079       
                                                                                                                      
Partners' Distributions                              (25,563)                  (6,063)                  (19,500)      
                                                                                                                      
Net Income (Loss)                                    (39,718)                  18,130                   (57,848)      
                                             ------------------       ------------------          ----------------    
Balance March 31, 1999                       $      1,610,138         $     2,134,756             $    (524,618)      
                                             ==================       ==================          ================          
</TABLE> 

                            See Accompanying Notes

                                       5
<PAGE>
 
                     Texland Drilling Program - 1981, Ltd.
                            (A Limited Partnership)

                            Statements of Cash Flow
                  Three Months Ended March 31, 1999 and 1998
                                  (Unaudited)

<TABLE> 
<CAPTION>                                                                                                 
                                                                                    1999                        1998
                                                                              ------------------       -------------------    
<S>                                                                           <C>                      <C>              
Cash Flows from Operating Activities
   Net Income (Loss)                                                          $       (39,718)         $       25,779
   Adjustments to Reconcile Net Income to Net Cash Provided by                                  
      Operating Activities:                                                                     
      Depreciation, Depletion and Amortization Expenses                                80,044                  78,905
      Abandoned Leaseholds                                                                      
      Loss on Sale of Assets                                                                    
      Change in Accounts Receivable                                                        72                  37,999
      Change in Accounts Payable                                                       (2,929)                 (5,481)
                                                                              -----------------        -----------------
      Total Adjustments                                                                77,187                 111,423   
                                                                              -----------------        -----------------
      Net Cash Provided by Operating Activities                                        37,468                 137,202   
                                                                                                                        
Cash Flows from Investing Activities                                                                                    
   Acquisition of Property and Equipment                                               (2,079)                 (6,229)  
   Proceeds from Sale of Property and Equipment                                             -                       -   
                                                                              -----------------        -----------------
      Net Cash Used by Investing Activities                                            (2,079)                 (6,229)  
                                                                                                                        
Cash Flows from Financing Activities                                                                                    
   Partners' Contributions                                                              2,079                   5,596   
   Partners' Distributions                                                            (25,563)               (137,150)  
                                                                              -----------------        -----------------
      Net Cash Used by Financing Activities                                           (23,483)               (131,554)  
                                                                                                                        
Net Increase in Cash                                                                   11,906                    (581)  
Cash at Beginning of Year                                                               8,308                  63,132   
                                                                              -----------------        -----------------
Cash at End of Quarter                                                        $        20,214          $       62,551   
                                                                              =================        =================
</TABLE> 

                            See Accompanying Notes

                                       6
<PAGE>
 
                      Texland Drilling Program-1981, Ltd.
                            (A Limited Partnership)

                         Notes To Financial Statements
                                March 31, 1999
                                  (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, Ltd.
                            (A Limited Partnership)

                   Notes To Financial Statements(Continued)
                                March 31, 1999
                                  (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, 1999  and March 31, 1998, the Partnership
was charged $42,963 and $46,298 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, Ltd.
                            (A Limited Partnership)

              Management's Discussion And Analysis Of Financial 
                      Condition And Results Of Operations
                               
                                March 31, 1999

The Partnership's average price per barrel of oil for the first quarter of 1999
was $7.24 as compared to $10.69 for the first quarter of 1998. The decreased
revenue and related severance tax expense result primarily from the decrease in
average oil prices.

Production expenses for 1999 decreased from the comparable period in 1998, due
to decreased remedial workover activity. In addition, several wells were shut-
in temporarily due to low oil prices.

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, Ltd.



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



Date: May 14, 1999

                                       10