<PAGE>   1
                                    FORM 10-Q

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D. C. 20549

(Mark One)

[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 number                            1-737
                       --------------------------------------------------------



                            TEXAS PACIFIC LAND TRUST
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)


           NOT APPLICABLE                                  75-0279735
--------------------------------------------------------------------------------
   (State or other jurisdiction of                     (I.R.S. Employer
    incorporation or organization)                    Identification No.)

              80 Broad Street, Suite 2700, New York, New York 10004
--------------------------------------------------------------------------------
                    (Address of principal executive offices)
                                   (Zip Code)


                                  212/269-2266
--------------------------------------------------------------------------------
              (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 [ ]


<PAGE>   2


                                     Part I
                              FINANCIAL INFORMATION
                            TEXAS PACIFIC LAND TRUST
                                 BALANCE SHEETS
                      MARCH 31, 1998 and DECEMBER 31, 1997
                      ------------------------------------
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                                                                  March 31,      December 31,
     ASSETS                                                                                         1998             1997
                                                                                                ------------     ------------
<S>                                                                                             <C>              <C>         
Cash                                                                                            $    393,017     $    112,591
Temporary cash investments at cost which approximates market                                       2,150,000        1,800,000
Accounts receivable                                                                                  386,263          386,781
Accrued interest receivable                                                                          446,858          411,674
Prepaid expenses                                                                                      31,850           45,500
Notes receivable for land sales                                                                   10,201,360        9,307,218
Real estate acquired through foreclosure:
      (27,585.95 acres at March 31, 1998 and December 31, 1997)                                    4,466,895        4,466,895
Water wells, leasehold improvements, furniture and
       equipment - at cost less accumulated depreciation                                             120,999          142,630

Property, no value assigned (note 2):
     Land (surface rights) situated in twenty-one counties in
         Texas - 1,041,792.77 acres in 1998 and 1,065,481.33 acres in 1997                                --               --

     Town lots in Iatan, Loraine and Morita - 628 lots in 1998 and 1997                                   --               --

     1/16 nonparticipating perpetual royalty interest in 386,987.70 acres in 1998 and 1997                --               --

     1/128 nonparticipating perpetual royalty interest in 85,413.60 acres in 1998 and 1997                --               --
                                                                                                ------------     ------------
                                                                                                $ 18,197,242     $ 16,673,289
                                                                                                ============     ============

     LIABILITIES AND CAPITAL

Federal income taxes payable                                                                    $    695,189     $     42,783
Other taxes payable                                                                                   97,094           24,372
Other liabilities                                                                                    186,487           93,072
Escrow deposits on land sales                                                                          2,000               --
Deferred taxes                                                                                     4,571,360        4,291,856
                                                                                                ------------     ------------
          Total liabilities                                                                        5,552,130        4,452,083

Capital (note 3)
      Certificates of Proprietary Interest, par value $100
            each; outstanding one certificate in 1998 and 1997                                            --               --

      Sub-share Certificates in Certificates of Proprietary Interest, par value
            $.16 2/3 each; outstanding 2,739,505 sub-shares in 1998 and
            2,753,205 sub-shares in 1997                                                                  --               --

      Net proceeds from all sources                                                               12,645,112       12,221,206
                                                                                                ------------     ------------
           Total capital                                                                          12,645,112       12,221,206

                                                                                                ------------     ------------
                                                                                                $ 18,197,242     $ 16,673,289
                                                                                                ============     ============
</TABLE>


                 See accompanying notes to financial statements.

                                       (1)

<PAGE>   3


                            TEXAS PACIFIC LAND TRUST
                              STATEMENTS OF INCOME
                            ------------------------

                                   (Unaudited)


<TABLE>
<CAPTION>
                                                     Three Months Ended
                                                          March 31
                                                 -------------------------
                                                    1998           1997
                                                 ----------     ----------
<S>                                              <C>            <C>       
Income:
     Rentals, royalties and sundry income        $1,465,516     $1,285,946
     Land sales                                   1,879,400      2,188,172
     Interest                                       244,834        168,868
                                                 ----------     ----------
                                                  3,589,750      3,642,986
                                                 ----------     ----------

Expenses:
     Taxes, other than Federal income taxes         124,418        152,435
     General and administrative expenses            347,643        299,056
                                                 ----------     ----------
                                                    472,061        451,491
                                                 ----------     ----------

            Income before provision for
                 Federal income taxes             3,117,689      3,191,495

Provision for Federal income taxes (note 4)         976,036      1,014,168
                                                 ----------     ----------

                 Net income                      $2,141,653     $2,177,327
                                                 ==========     ==========

Average number of sub-share certificates
       and equivalent sub-share certificates
       outstanding                                2,750,988      2,842,905
                                                 ==========     ==========

Earnings per sub-share certificate               $      .78     $      .77
                                                 ==========     ==========

Cash dividend per sub-share certificate          $      .40     $      .40
                                                 ==========     ==========
</TABLE>


                 See accompanying notes to financial statements.




                                       (2)

<PAGE>   4
                            TEXAS PACIFIC LAND TRUST
                            STATEMENTS OF CASH FLOWS
                            ------------------------  
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                                       Three Months Ended
                                                                                            March 31
                                                                                  ----------------------------
                                                                                     1998             1997
                                                                                  -----------      -----------
<S>                                                                               <C>              <C>        
Cash flows from operating activities:

    Net income                                                                    $ 2,141,653      $ 2,177,327

        Adjustments to reconcile net income to net cash provided by operating
            activities:

                 Depreciation                                                          28,500           10,050
                 Deferred taxes                                                       279,504          347,798

                 (Increase) decrease in assets:
                    Accounts receivable                                                   518              889
                    New notes from land sales                                      (1,329,000)      (1,311,203)
                    Payments received on notes receivable                             434,858          296,507
                    Accrued interest receivable                                       (35,184)         (56,181)
                    Prepaid expenses                                                   13,650           13,722
                  Increase in liabilities:
                    Federal income taxes                                              652,406          563,427
                    Other taxes                                                        72,722           87,196
                    Escrow deposits on land sales                                       2,000           27,000
                    Other liabilities                                                  93,415           23,617
                                                                                  -----------      -----------

                        Total adjustments                                             213,389            2,822
                                                                                  -----------      -----------

                            Net cash provided by operating activities               2,355,042        2,180,149
                                                                                  -----------      -----------

Cash flows from investing activities:
   Additions to water wells, leasehold improvements,
          furniture and equipment                                                      (6,869)         (20,569)
                                                                                  -----------      -----------

Cash flows from financing activities:
    Sub-shares purchased for retirement                                              (614,945)        (651,578)
    Dividends paid                                                                 (1,102,802)      (1,134,882)
                                                                                  -----------      -----------

                         Net cash used by financing activities                     (1,717,747)      (1,786,460)
                                                                                  -----------      -----------

Net increase in cash and cash equivalents                                             630,426          373,120

Cash and cash equivalents at beginning
    of year                                                                         1,912,591        1,794,898
                                                                                  -----------      -----------
Cash and cash equivalents at end
    of period                                                                     $ 2,543,017      $ 2,168,018
                                                                                  ===========      ===========
</TABLE>


                 See accompanying notes to financial statements.


                                       (3)

<PAGE>   5


                                    TEXAS PACIFIC LAND TRUST
                                  NOTES TO FINANCIAL STATEMENTS
                                         MARCH 31, 1998
                                  -----------------------------



(1)      In the opinion of management, the accompanying unaudited financial
         statements contain all adjustments (consisting of only normal recurring
         accruals) necessary to present fairly the financial position of Texas
         Pacific Land Trust (Trust) as of March 31, 1998 and December 31, 1997
         and the results of its operations and its cash flows for the three
         months ended March 31, 1998 and March 31, 1997, respectively. These
         financial statements and footnotes included herein should be read in
         conjunction with the Trust's annual financial statements as of December
         31, 1997 and 1996 and for each of the years in the three year period
         ended December 31, 1997 included in the Trust's Form 10-K.

(2)      No value is assigned to the land, unless acquired through foreclosure;
         consequently, no allowance for depletion is computed, and no charge to
         income is made therefor, and no cost is deducted from the proceeds of
         the land sales in computing gain or loss thereon.

(3)      The Sub-shares and the Certificates of Proprietary Interest are freely
         interchangeable in the ratio of one Certificate of Proprietary Interest
         for 600 Sub-shares or 600 Sub-shares for one Certificate of Proprietary
         Interest.

(4)      The Trust's effective Federal income tax rate is less than the 34%
         statutory rate because taxable income is reduced by statutory
         percentage depletion allowed on mineral royalty income.

(5)      The results of operations for the three months ended March 31, 1998 are
         not necessarily indicative of the results to be expected for the full
         year.

(6)      Cash in excess of daily requirements is invested in money market
         instruments with maturities of ninety days or less. Such investments
         are deemed to be cash equivalents for purposes of the statements of
         cash flows.

         Supplemental cash flow information for the three months ended March
         31, 1998 and 1997 is summarized as follows:

<TABLE>
<CAPTION>
                                                        1998           1997
                                                    -----------    -----------
<S>                                                 <C>            <C>        
         Federal income taxes paid                  $    44,126    $   102,943
                                                    ===========    ===========
</TABLE>

         There were no non-cash investing and financing activities during the
         three months ended March 31, 1998 and 1997.



                                       (4)

<PAGE>   6
                           Management's Discussion and
                       Analysis of Financial Condition and
                          Results of Operations for the
                               Three Months Ended
                             March 31, 1998 and 1997
                       -----------------------------------


Earnings per sub-share were $.78 for the first quarter of 1998 compared with
$.77 in the first quarter of 1997.

Total revenues for the first quarter of 1998 were $3,589,750 compared with
$3,642,986 in the first quarter of 1997, a decrease of 1.5%.

The Trust sold 23,688 acres of land for a total of $1,879,400, an average of $79
per acre, in the first quarter of 1998. In the comparable period of 1997 a total
of 5,839.39 acres were sold for $2,188,172, an average of $375 per acre.

Land Sales may vary widely from year to year and quarter to quarter. The total
dollar amount, the average price per acre, and the number of acres sold in any
one year or quarter should not be assumed to be indicative of land sales in the
future. The Trust is a passive seller of land; it does not actively solicit
sales of land. The demand for and the sales price of any particular tract of the
Trust's land is influenced by many factors including the national and local
economies, the rate of residential and commercial development in nearby areas,
livestock carrying capacity, and the conditions of the local agricultural
industry which itself is influenced by range conditions and prices for livestock
and other agricultural products. Approximately 99% of the Trust's land is
classified as ranch land and intermingled with other ownerships to form ranching
units. Ranch land sales are, therefore, largely dependent on the actions of the
adjoining landowners.

Rentals, royalties and sundry income amounted to $1,465,516 in the first quarter
of 1998, an increase of 14.0% compared with the first quarter of 1997.

Oil and gas royalty revenue was $754,987, down 28.5% compared with the first
quarter of 1997. Oil royalty revenue was $509,248, down 28.0% compared with
1997. Crude oil production subject to the Trust's royalty interest was up 3.9%
in the first quarter, and the average price per barrel was down 30.7% compared
with 1997. Gas royalty revenue was $245,739 in the first quarter, down 29.5% on
a volume decrease of 1.1% and a price decrease of 28.5%.

Easement and Sundry income was $623,010 up 348.2% over the first quarter of
1997. This was mainly due to increases in pipeline easement and seismic permit
income neither of which are recurring or can be predicted.

Interest revenue increased 45.0% in the first quarter of 1998, compared with
1997. Interest from notes receivable amounted to $210,695, an increase of 51.4%.
Notes receivable were $10,201,360 as of March 31, 1998, an increase of 67.7% for
the comparable period due to substantial land sales made in 1997, of which a
portion was financed by the Trust. Sundry interest was $34,139, up 14.8%
compared with 1997.

Taxes, other than Federal taxes on income, were down 18.4% due to a decrease in
land inventory and a decrease in royalty income in the first quarter of 1998 
compared with last year.

General and administrative expenses increased due to an increase in depreciation
expense related to the purchase of computer hardware and software.




                                       (5)
<PAGE>   7
Management's Discussion (cont'd)

The Trust's oil and gas royalty revenues, lease rentals and receipts of
interest and principal on notes receivable has generated more than adequate
amounts of cash to meet the Trust's needs and should continue to do so in the
predictable future.



                                      (6)
<PAGE>   8


                                     PART II


                                OTHER INFORMATION


Item 6.   Exhibits and Reports on Form 8-K

          (a)  Exhibits. Interim report furnished to shareholders upon request
               per sub-part Item 601 (19) Regulation S-K.

               Exhibit 27 - Financial Data Schedule.

          (b)  Reports on Form 8-K. The registrant has filed no reports on Form
               8-K during the quarter for which this report is filed.



                                   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.



                                               TEXAS PACIFIC LAND TRUST
                                           ----------------------------------
                                                     (Registrant)



             Date 5/14/98              By  /s/ ROY THOMAS
                 -------------------       ----------------------------------
                                           Roy Thomas, General Agent,
                                           Authorized Signatory and Principal
                                           Financial Officer



                                       (7)

<PAGE>   9


                                INDEX TO EXHIBITS




<TABLE>
<CAPTION>
EXHIBIT
NUMBER                          EXHIBIT
-------                         -------

  <S>                <C>
  27                 Financial Data Schedule
</TABLE>