<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, 2000
                                                 --------------

                                       OR

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

             For the transition period from _________ to _________.


                        For Quarter Ended March 31, 2000
                                          --------------

                         Commission File number 2-71058
                                                -------

                          DAWSON GEOPHYSICAL COMPANY
             -------------------------------------------------------
             (Exact name of Registrant as specified in its Charter)

              TEXAS                                       75-0970548
-------------------------------               --------------------------------
(State or other jurisdiction of               (IRS Employer Identification No.)
 incorporation or organization)


508 West Wall, Suite 800, Midland, Texas                    79701
----------------------------------------                  ----------
(Address of principal executive offices)                  (Zip Code)


        (Registrant's telephone number, including area code) 915/684-3000
                                                             ------------

                                      NONE
                                  ------------
(Former Name, Former Address & 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    .
                                              ---      ---


  Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date.


             CLASS                              Outstanding at March 31, 2000.
--------------------------------                ------------------------------
Common Stock, $.33 1/3 par value                       5,428,794 shares



                                       -1-


<PAGE>   2


                           DAWSON GEOPHYSICAL COMPANY

                                      INDEX


<TABLE>
<CAPTION>
                                                                                       Page No.
                                                                                       --------
<S>                                                                                  <C>
Part I.           Financial Information:

Item 1.  Financial Statements

                  Statements of Operations --
                        Three Months and Six Months
                           ended March 31, 2000 and 1999                                    3

                  Balance Sheets --
                        March 31, 2000 and September 30,
                        1999                                                                4

                  Statements of Cash Flows --
                        Six Months Ended March 31,
                        2000 and 1999                                                       5

                  Notes to Financial Statements                                             6

Item 2.           Management's Discussion and Analysis of
                        Financial Condition and Results of
                        Operations                                                          8


Item 3.           Quantitative and Qualitative Disclosures
                        About Market Risk                                                   10
</TABLE>



                                       -2-



<PAGE>   3



                          PART I. FINANCIAL INFORMATION

                           DAWSON GEOPHYSICAL COMPANY

                            STATEMENTS OF OPERATIONS
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                            Three Months Ended                 Six Months Ended
                                                  March 31                         March 31
                                       -----------------------------     -----------------------------
                                            2000             1999             2000             1999
                                       ------------     ------------     ------------     ------------
<S>                                    <C>              <C>              <C>              <C>
Operating revenues                     $  4,275,000     $  6,053,000     $  9,168,000     $ 14,071,000
                                       ------------     ------------     ------------     ------------
Operating costs:
         Operating expenses               5,104,000        5,308,000       10,634,000       11,741,000
         General and administrative         668,000          494,000        1,431,000        1,040,000
         Depreciation                     2,473,000        2,698,000        4,936,000        5,409,000
                                       ------------     ------------     ------------     ------------
                                          8,245,000        8,500,000       17,001,000       18,190,000
                                       ------------     ------------     ------------     ------------
Loss from operations                     (3,970,000)      (2,447,000)      (7,833,000)      (4,119,000)

Other income (expense):

         Interest income                    235,000          212,000          463,000          398,000
         Loss on disposal of assets              --          (23,000)              --          (12,000)
         Other income                         3,000           36,000            3,000           42,000
                                       ------------     ------------     ------------     ------------

Loss before income tax                   (3,732,000)      (2,222,000)      (7,367,000)      (3,691,000)
Income tax benefit (expense)                712,000          761,000        1,948,000        1,256,000
                                       ------------     ------------     ------------     ------------

Net loss                               $ (3,020,000)    $ (1,461,000)    $ (5,419,000)    $ (2,435,000)
                                       ============     ============     ============     ============

Net loss per common share              $       (.56)    $       (.27)    $      (1.00)    $       (.45)
                                       ============     ============     ============     ============


Weighted average equivalent common
    shares outstanding                    5,428,772        5,406,416        5,421,627        5,387,397
                                       ============     ============     ============     ============
</TABLE>



See accompanying notes to the financial statements.


                                       -3-



<PAGE>   4
                           DAWSON GEOPHYSICAL COMPANY

                                 BALANCE SHEETS


<TABLE>
<CAPTION>
                                                             March 31, 2000   September 30, 1999
                                                             --------------   ------------------
                                                              (unaudited)
<S>                                                           <C>                <C>
ASSETS
Current assets:
   Cash and cash equivalents                                  $  3,506,000       $  4,993,000
   Short-term investments                                       13,530,000         13,547,000
   Accounts receivable,net of allowance
         for doubtful accounts of $493,000
         in 2000 and $133,000 in 1999                            5,913,000          5,567,000
   Income taxes receivable                                       1,475,000          1,668,000
   Prepaid expenses                                                186,000            466,000
                                                              ------------       ------------

           Total current assets                                 24,610,000         26,241,000
                                                              ------------       ------------

Property, plant and equipment                                   70,725,000         71,706,000
   Less accumulated depreciation                               (40,539,000)       (36,529,000)
                                                              ------------       ------------

           Net property, plant and equipment                    30,186,000         35,177,000
                                                              ------------       ------------


                                                              $ 54,796,000       $ 61,418,000
                                                              ============       ============

LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
   Accounts payable                                           $    408,000       $    778,000
   Accrued liabilities:
      Payroll costs and other taxes                                163,000            506,000
      Other                                                         40,000             21,000
                                                              ------------       ------------

           Total current liabilities                               611,000          1,305,000
                                                              ------------       ------------

Deferred income taxes                                                   --            645,000

Stockholders' equity:
   Preferred stock--par value $1.00 per share;
        5,000,000 shares authorized, none outstanding                   --                 --
   Common stock - par value $.33 1/3 per share;
       10,000,000 shares authorized, 5,428,794
       and 5,406,794 issued and outstanding
       respectively                                              1,810,000          1,802,000
   Additional paid-in capital                                   38,624,000         38,497,000
   Retained earnings                                            13,751,000         19,169,000
                                                              ------------       ------------

           Total stockholders' equity                           54,185,000         59,468,000
                                                              ------------       ------------

                                                              $ 54,796,000       $ 61,418,000
                                                              ============       ============
</TABLE>


Contingencies (See Note 2)

See accompanying notes to the financial statements.


                                       -4-

<PAGE>   5


                           DAWSON GEOPHYSICAL COMPANY

                            STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                Six Months Ended
                                                                    March 31
                                                        -------------------------------
                                                            2000               1999
                                                        ------------       ------------
<S>                                                     <C>                <C>
Cash flows from operating activities:
         Net loss                                       $ (5,419,000)      $ (2,435,000)

Adjustments to reconcile net income to net cash
  provided by (used in) operating activities:
         Depreciation                                      4,936,000          5,409,000
         Loss on disposal of assets                               --             12,000
         Non-cash interest income                                 --            (11,000)
         Non-cash compensation                               101,000            256,000
         Deferred income taxes                              (474,000)           205,000
         Other                                               201,000            160,000
         Change in current assets and liabilities:
           Decrease (increase) in accounts
             receivable                                     (346,000)         5,361,000
           Decrease in prepaid expenses                      280,000             24,000
           Decrease (increase) in income taxes
                   receivable                                 22,000           (434,000)
           Decrease in accounts payable                     (370,000)        (1,189,000)
           Decrease in accrued liabilities                  (322,000)        (1,041,000)
                                                        ------------       ------------

Net cash provided by (used in)
         operating activities                             (1,391,000)         6,317,000
                                                        ------------       ------------

Cash flows from investing activities:
  Proceeds from disposal of assets                                --             16,000
  Capital expenditures                                      (130,000)          (134,000)
  Proceeds from maturity of short-term
         investments                                       1,000,000          1,000,000
   Investment in short-term investments                     (998,000)          (978,000)
                                                        ------------       ------------

Net cash used in investing activities                       (128,000)           (96,000)
                                                        ------------       ------------

Cash flows from financing activities:
  Proceeds from exercise of stock options                     32,000                 --
                                                        ------------       ------------

Net cash provided by financing activities                     32,000                 --
                                                        ------------       ------------

Net increase (decrease) in cash and cash
  equivalents                                             (1,487,000)         6,221,000

Cash and cash equivalents at beginning
  of period                                                4,993,000          5,745,000
                                                        ------------       ------------

Cash and cash equivalents at end of period              $  3,506,000       $ 11,966,000
                                                        ============       ============
</TABLE>


See accompanying notes to the financial statements.


                                       -5-


<PAGE>   6


                           DAWSON GEOPHYSICAL COMPANY

                          NOTES TO FINANCIAL STATEMENTS


1.       OPINION OF MANAGEMENT

         Although the information furnished is unaudited, in the opinion of
management of the Registrant, the accompanying financial statements reflect all
adjustments (consisting only of normal recurring accruals) necessary for a fair
presentation of the financial condition and results of operations for the
periods presented. The results of operations for the three months and the six
months ended March 31, 2000, are not necessarily indicative of the results to be
expected for the fiscal year.

2.       CONTINGENCIES

         The Company is a defendant in two lawsuits pending in the 112th and
83rd District Courts of Pecos County, Texas (respectively, Cause No. 8812,
Ernestine Bernal, et al. Vs. Javier Antonio Orona, et al.; and Cause No.
P5565-83-CV, Carla Jaquez, et al. Vs. Javier Antonio, et al.) relating to a July
1995 accident involving a van owned by the Company which was used to transport
employees to various job sites and a non-Company owned vehicle. The accident
resulted in the deaths of four Company employees who were passengers in such
van. The Company is one of several named defendants in such suits. Other named
defendants include the estate of the deceased driver of such van, who was an
employee of the Company, the driver of such non-Company owned vehicle, who was
then an employee of the Company, the owner of such vehicle, and Ford Motor
Company, the manufacturer of the Company van involved in such accident. In
general, the claims against the Company include allegations of negligence, gross
negligence and/or intentional tort as a result of, among other things, the
Company's alleged failure to provide safe transportation for its employees and
to properly select, train and supervise the deceased driver of such van. The
plaintiffs in such suits are seeking actual damages from the defendants of $15.5
million, additional unspecified actual damages, prejudgment and post-judgment
interest and costs of suit as well as exemplary and punitive damages in an
amount not to exceed four times the amount of actual damages. The Company
believes that it has meritorious defenses to the claims asserted against it in
such suits and it intends to continue to vigorously defend itself against such
claims. In addition, the Company believes that it has approximately $11 million
of liability insurance coverage to provide against an unfavorable outcome. The
court has heard a motion for summary judgment in both cases, requesting that the
Company be dismissed from such suit based upon various legal theories. Such
motion has not yet been ruled on by the court. Due to the uncertainties inherent
in litigation, no assurance can be given as to the ultimate outcome of such
suits or the adequacy or availability of the Company's liability insurance to
cover the damages, if any, which may be assessed against the Company in such
suits. A judgment awarding plaintiffs an amount significantly exceeding the
Company's available insurance coverage could have a material adverse effect on
the Company's financial condition, results of operations and liquidity.

         The Company is party to other legal actions arising in the ordinary
course of its business, none of which management believes will result in a
material adverse effect on the Company's financial position or results of
operation, as the Company believes it is adequately insured.

                                       -6-



<PAGE>   7
3.       NET INCOME PER COMMON SHARE

         The following table sets forth the computation of basic and diluted net
income per common share:


<TABLE>
<CAPTION>
                                                Three Months Ended              Six Months Ended
                                                     March 31                        March 31
                                           ----------------------------    ----------------------------
                                               2000            1999            2000            1999
                                           ------------    ------------    ------------    ------------
<S>                                        <C>             <C>             <C>             <C>
Numerator:
  Net loss and numerator for basic
    and diluted net income per
    common share-income available
    to common stockholders                 $ (3,020,000)   $ (1,461,000)   $ (5,419,000)   $ (2,435,000)
                                           ------------    ------------    ------------    ------------

Denominator:
  Denominator for basic net loss
    per common share-weighted
    average common shares                     5,428,772       5,406,416       5,421,627       5,387,397
  Effect of dilutive securities-
    employee stock options                           --              --              --              --
                                           ------------    ------------    ------------    ------------
  Denominator for diluted net
    loss per common share-
    adjusted weighted average
    common shares and assumed
    conversions                               5,428,772       5,406,416       5,421,627       5,387,397
                                           ------------    ------------    ------------    ------------

Net income (loss) per common share         $       (.56)   $       (.27)   $      (1.00)   $       (.45)
                                           ============    ============    ============    ============

Net income (loss) per common
  share--assuming dilution                 $       (.56)   $       (.27)   $      (1.00)   $       (.45)
                                           ============    ============    ============    ============
</TABLE>


         Employee stock options to purchase shares of common stock were
outstanding during fiscal year 2000 and 1999 but were not included in the
computation of diluted net loss per share because either (i) the employee stock
options' exercise price was greater than the average market price of the common
stock of the Company, or (ii) the Company had a net loss from continuing
operations and, therefore, the effect would be antidilutive.


                                       -7-

<PAGE>   8

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


The following discussion should be read in conjunction with the Company's
financial statements. In addition, in reviewing the Company's financial
statements it should be noted that the Company's revenues relate to oil and gas
exploration and production activity and fluctuations in the Company's results of
operations may occur due to commodity prices, weather, land use permitting and
other factors.

FORWARD LOOKING STATEMENTS

All statements other than statements of historical fact included in this report,
including without limitation, statements under "Management's Discussion and
Analysis of Financial Condition and Results of Operations" regarding the
Company's financial position, business strategy and plans and objectives of
management of the Company for future operations, are forward-looking statements
within the meaning of Section 27A of the Securities Act of 1933 and Section 21E
of the Securities Exchange Act of 1934. When used in this report, words such as
"anticipate", "believe", "estimate", "expect", "intend", and similar
expressions, as they relate to the Company or its management, identify
forward-looking statements. Such forward-looking statements are based on the
beliefs of the Company's management as well as assumptions made by and
information currently available to the Company's management. Actual results
could differ materially from those contemplated by the forward-looking
statements as a result of certain factors, including but not limited to
dependence upon energy industry spending, weather problems, inability to obtain
land use permits, the volatility of oil and gas prices, and the availability of
capital resources. Such statements reflect the current views of the Company with
respect to future events and are subject to these and other risks, uncertainties
and assumptions relating to the operations, results of operations, growth
strategy and liquidity of the Company. All subsequent written and oral
forward-looking statements attributable to the Company or persons acting on its
behalf are expressly qualified in their entirety by this paragraph. The Company
assumes no obligation to update any such forward-looking statements.


RESULTS OF OPERATIONS

The Company's operating revenues for the first six months of fiscal 2000 totaled
$9,168,000 versus $14,071,000 for the same period of fiscal 1999, a decrease of
35%. For the three months ended March 31, 2000, operating revenues totaled
$4,275,000 versus $6,053,000 for the same period of fiscal 1999, a decrease of
29%. Demand for the Company's services continues to be negatively impacted by
reduced activity in the petroleum exploration industry. With a capacity to
operate six crews, the Company operated four crews in the first quarter of
fiscal 2000 and reduced the number of operating crews to two in March 2000. In
addition to the decrease in the number of operating crews, the decrease in
revenues reflects severe price competition.



                                       -8-

<PAGE>   9


Operating expenses for the six months ended March 31, 2000 totaled $10,634,000,
a decrease of 9% from the same period of fiscal 1999. For the quarter ended
March 31, 2000, operating expenses totaled $5,104,000 versus $5,308,000 for the
same period of fiscal 1999. In January 1999 the Company enacted employee layoffs
and salary reductions; however, the Company has retained key technical and
professional personnel. For the first six months of fiscal 2000 the Company
averaged 3.6 operating crews as compared to 4 operating crews for the same
period of fiscal 1999.

General and administrative expenses for the six months ended March 31, 2000
totaled $1,431,000 as compared to $1,040,000 for the same period of fiscal 1999.
For the quarter ended March 31, 2000, general and administrative expenses
totaled $668,000, an increase of $174,000 over the same period of fiscal 1999.
The increase primarily consists of a provision for doubtful accounts of $360,000
recognized during the six months ended March 31, 2000. A provision for doubtful
accounts was not recognized in the prior fiscal year until May 1999.

Depreciation for the six months ended March 31, 2000 totaled $4,936,000, a
decrease of 9% from the same period of fiscal 1999. For the quarter ended March
31, 2000, depreciation decreased $225,000, or 8%. Depreciation decreased as a
result of a suspension of capital expenditures during fiscal 1999 due to
industry conditions.

Total operating costs for the first six months of fiscal 2000 were $17,001,000,
a decrease of 6.5%, from the same period of fiscal 1999 due to the factors
described above. For the quarter ended March 31, 2000, total operating costs
were consistent with the same period of the prior fiscal year. The 35% decrease
of revenues as compared to the 6.5% decrease of total operating costs for the
first six months ended March 31, 2000 reflects the high proportion of relatively
fixed total operating costs (including personnel costs of active crews and
depreciation costs) inherent in the Company's business and continued fierce
price competition in the bidding process for geophysical services.

The Company currently anticipates an annual effective tax benefit rate of 26%
primarily as a result of establishing a deferred tax valuation allowance in the
current year.

LIQUIDITY AND CAPITAL RESOURCES

Cash Flows

Net cash used in operating activities of $1,391,000 for the six months ended
March 31, 2000 primarily reflects the net loss for the quarter offset by changes
in working capital components and the decrease in deferred income taxes. The
decrease in deferred income taxes in fiscal 2000 is a result of the reversal of
temporary differences due to depreciation and recognition of net operating loss
carryback.

Net cash used in investing activities for the six months ended March 31, 2000 is
consistent with the same period of the prior year representing management of
short-term investments and severely limited capital expenditures.


                                       -9-


<PAGE>   10

The cash flows provided by financing activities for the six months ended March
31, 2000 represent the proceeds from the exercise of a stock option.

Capital Expenditures

The Company continually strives to supply market demand with technologically
advanced 3-D data acquisition recording systems and leading edge data processing
capabilities. Capital expenditures for fiscal 1999 were minimal in comparison to
the capital expansion effort in fiscal 1998 and the five prior fiscal years.
Depreciation increased each fiscal year through 1999 as a new crew as well as
additions and replacements of cables and geophones, vehicles, and other data
acquisition equipment has been placed into service each year for the past
several years. Depreciation for fiscal 2000 is expected to be less than in
fiscal 1999 due to the restricted capital expenditures of fiscal 1999. The
Company will maintain equipment in and out of service in anticipation of
increased future demand of the Company's services.


Capital Resources

The Company believes that its capital resources including its short-term
investments and cash flow from operations are adequate to meet its current
operational needs and finance capital needs as determined by market demand and
technological developments.

LITIGATION

The Company is a defendant in two lawsuits relating to a July 1995 accident
involving a van owned by the Company in which four Company employees died. The
Company believes that it has meritorious defenses to the claims asserted against
it in such suits. Further, while the plaintiffs seek damages in excess of the
Company's liability insurance policies, the Company believes that its liability
insurance should provide adequate coverage of the damages, if any, which may be
assessed against the Company in such litigation. Due to the uncertainties
inherent in litigation, no assurance can be given as to the ultimate outcome of
such suits or the adequacy or availability of the Company's liability insurance
to cover any such damages. A judgment awarding plaintiffs an amount
significantly exceeding the Company's available insurance coverage could have a
material adverse effect on the Company's financial condition, results of
operations and liquidity.


Item 3. Quantitative and Qualitative Disclosure About Market Risk

The primary sources of market risk include fluctuations in commodity prices
which effect demand for and pricing of the Company's services and interest rate
fluctuations. At March 31, 2000 the Company had no indebtedness and in addition
the Company's short-term investments were fixed-rate and, therefore, do not
expose the Company to significant risk of earnings or cash flow loss due to
changes in market interest rate. The Company has not entered into any hedge
arrangements, commodity swap agreements, commodity futures, options or other
derivative financial instruments. The Company does not currently conduct
business internationally so it is generally not subject to foreign currency
exchange rate risk.

                                      -10-


<PAGE>   11

                                    SIGNATURE




                              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.



                                             DAWSON GEOPHYSICAL COMPANY
                                             --------------------------
                                             (REGISTRANT)


                                             By: /s/ L. Decker Dawson
                                                 -------------------------
                                             L. Decker Dawson
                                             President



                                             /s/ Christina W. Hagan
                                             -----------------------------
                                             Christina W. Hagan
                                             Chief Financial Officer


DATE: April 26, 2000



                                      -11-



<PAGE>   12


                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
Exhibit No.                        Description
-----------                        -----------
<S>                          <C>
    27                       Financial Data Schedule
</TABLE>