<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 June 30, 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 June 30, 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 June 30, 2000
   --------------------------------              ----------------------------
   Common Stock, $.33 1/3 par value                     5,428,794 shares


<PAGE>   2
                           DAWSON GEOPHYSICAL COMPANY

                                     INDEX

<TABLE>
<CAPTION>

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

Item 1.           Financial Statements:

                  Statements of Operations --
                        Three Months and Nine Months
                           ended June 30, 2000 and 1999                                     3

                  Balance Sheets --
                        June 30, 2000 and September 30,
                        1999                                                                4

                  Statements of Cash Flows --
                        Nine Months Ended June 30,
                        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

Part II.          Other Information                                                        11
</TABLE>


                                      -2-
<PAGE>   3
                         PART I. FINANCIAL INFORMATION

                           DAWSON GEOPHYSICAL COMPANY

Item 1.  Financial Statements

                            STATEMENTS OF OPERATIONS
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                            Three Months Ended                   Nine Months Ended
                                                  June 30                             June 30
                                       ------------------------------      ------------------------------
                                           2000              1999              2000              1999
                                       ------------      ------------      ------------      ------------

<S>                                    <C>               <C>               <C>               <C>
Operating revenues                     $  2,712,000      $  4,575,000      $ 11,880,000      $ 18,646,000
                                       ------------      ------------      ------------      ------------
Operating costs:
      Operating expenses                  4,192,000         4,425,000        14,826,000        16,166,000
      General and administrative            508,000           610,000         1,939,000         1,650,000
      Depreciation                        2,189,000         2,631,000         7,125,000         8,040,000
                                       ------------      ------------      ------------      ------------
                                          6,889,000         7,666,000        23,890,000        25,856,000
                                       ------------      ------------      ------------      ------------

Loss from operations                     (4,177,000)       (3,091,000)      (12,010,000)       (7,210,000)

Other income (expense):

      Interest income                       291,000           242,000           754,000           640,000
      Gain (loss) on disposal
        of assets                            (9,000)            2,000            (9,000)          (10,000)
      Other income                           38,000            (1,000)           41,000            41,000
                                       ------------      ------------      ------------      ------------

Loss before income tax                   (3,857,000)       (2,848,000)      (11,224,000)       (6,539,000)

      Income tax benefit                    689,000           958,000         2,637,000         2,214,000
                                       ------------      ------------      ------------      ------------

Net loss                               $ (3,168,000)     $ (1,890,000)     $ (8,587,000)     $ (4,325,000)
                                       ============      ============      ============      ============

Net loss per common share              $       (.58)     $       (.35)     $      (1.58)     $       (.80)
                                       ============      ============      ============      ============

Weighted average equivalent common
    shares outstanding                    5,428,794         5,406,794         5,424,008         5,393,862
                                       ============      ============      ============      ============
</TABLE>



See accompanying notes to the financial statements.



                                      -3-
<PAGE>   4
                           DAWSON GEOPHYSICAL COMPANY

                                 BALANCE SHEETS

<TABLE>
<CAPTION>

                                                            June 30, 2000     September 30, 1999
                                                         ------------------   ------------------
                                                             (unaudited)
<S>                                                          <C>               <C>
ASSETS
Current assets:
   Cash and cash equivalents                                 $  5,793,000      $  4,993,000
   Short-term investments                                      13,527,000        13,547,000
   Accounts receivable, net of allowance for
         doubtful accounts of $553,000 in
         2000 and $133,000 in 1999                              2,322,000         5,567,000
   Income taxes receivable                                      2,165,000         1,668,000
   Prepaid expenses                                               243,000           466,000
                                                             ------------      ------------

           Total current assets                                24,050,000        26,241,000
                                                             ------------      ------------

Property, plant and equipment                                  69,554,000        71,706,000
   Less accumulated depreciation                              (41,556,000)      (36,529,000)
                                                             ------------      ------------

           Net property, plant and equipment                   27,998,000        35,177,000
                                                             ------------      ------------


                                                             $ 52,048,000      $ 61,418,000
                                                             ============      ============

LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
   Accounts payable                                          $    817,000      $    778,000
   Accrued liabilities:
      Payroll costs and other taxes                               211,000           506,000
      Other                                                         4,000            21,000
                                                             ------------      ------------

           Total current liabilities                            1,032,000         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 shares issued and outstanding
           in 2000 and 1999, respectively                       1,810,000         1,802,000
   Additional paid-in capital                                  38,624,000        38,497,000
   Retained earnings                                           10,582,000        19,169,000
                                                             ------------      ------------

           Total stockholders' equity                          51,016,000        59,468,000
                                                             ------------      ------------

                                                             $ 52,048,000      $ 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>

                                                            Nine Months Ended
                                                                  June 30
                                                       ------------------------------
                                                          2000               1999
                                                       ------------      ------------
<S>                                                    <C>               <C>
Cash flows from operating activities:
         Net loss                                      $ (8,587,000)     $ (4,325,000)

Adjustments to reconcile net loss to
  net cash provided by operating activities:
         Depreciation                                     7,125,000         8,040,000
         Loss on disposal of assets                           9,000            10,000
         Non-cash interest income                                --           (35,000)
         Non-cash compensation                              101,000           256,000
         Deferred income taxes                             (645,000)       (1,276,000)
         Provision for losses on trade
           receivables                                           --           120,000
         Other                                              207,000           248,000
         Change in current assets and liabilities:
           Decrease in accounts receivable                3,245,000         6,228,000
           Decrease in prepaid expenses                     223,000            42,000
           Increase in income taxes receivable             (497,000)         (104,000)
           Decrease (increase) in accounts
                   payable                                   39,000          (957,000)
           Decrease in accrued liabilities                 (313,000)       (1,164,000)
                                                       ------------      ------------

Net cash provided by operating activities                   907,000         7,083,000
                                                       ------------      ------------

Cash flows from investing activities:
  Proceeds from disposal of assets                          110,000            24,000
  Capital expenditures                                     (251,000)         (147,000)
  Proceeds from maturity of short-term
         investments                                      2,501,000         5,500,000
  Investment in short-term investments                   (2,499,000)      (11,507,000)
                                                       ------------      ------------

Net cash used in investing activities                      (139,000)       (6,130,000)
                                                       ------------      ------------

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


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

Net increase in cash and cash equivalents                   800,000           953,000

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

Cash and cash equivalents at end of period             $  5,793,000      $  6,698,000
                                                       ============      ============
</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 pre- sented. The results of operations for the three months and the
nine months ended June 30, 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                  Nine Months Ended
                                                 June 30                            June 30
                                       ----------------------------      ----------------------------
                                          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             $(3,168,000)     $(1,890,000)     $(8,587,000)     $(4,325,000)
                                       -----------      -----------      -----------      -----------

Denominator:
  Denominator for basic net loss
    per common share-weighted
    average common shares                5,428,794        5,406,794        5,424,008        5,393,862
  Effect of dilutive securities-
    employee stock options                      --               --               --               --
                                       -----------      -----------      -----------      -----------
  Denominator for diluted net
    loss per common share-
    adjusted weighted average
    common shares and assumed
    conversions                          5,428,794        5,406,794        5,424,008        5,393,862
                                       -----------      -----------      -----------      -----------

Net loss per common share              $      (.58)     $      (.35)     $     (1.58)     $      (.80)
                                       ===========      ===========      ===========      ===========

Net loss per common
  share--assuming dilution             $      (.58)     $      (.35)     $     (1.58)     $      (.80)
                                       ===========      ===========      ===========      ===========
</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 nine months of fiscal 2000
totaled $11,880,000 versus $18,646,000 for the same period of fiscal 1999, a
decrease of 36%. For the three months ended June 30, 2000, operating revenues
totaled $2,712,000 versus $4,575,000 for the same period of fiscal 1999, a
decrease of 41%. 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. The Company returned to four operating crews in July 2000. In
addition to the decreased number of crews operating during the quarter ended
June 30, 2000, the decrease in revenues reflects continuing severe price
competition.

                                      -8-
<PAGE>   9

Operating expenses for the nine months ended June 30, 2000 totaled $14,826,000,
a decrease of 8% from the same period of fiscal 1999. For the quarter ended
June 30, 2000, operating expenses totaled $4,192,000 versus $4,425,000 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.

General and administrative expenses for the nine months ended June 30, 2000
totaled $1,939,000 as compared to $1,650,000 for the same period of fiscal
1999. For the quarter ended June 30, 2000, general and administrative expenses
totaled $508,000, a decrease of $102,000 over the same period of fiscal 1999.
The decrease primarily represents a suspension of a provision for doubtful
accounts in May 2000, as the Company believes the allowance for doubtful
accounts is adequate. A provision for doubtful accounts was not recognized in
the prior fiscal year until May 1999.

Depreciation for the nine months ended June 30, 2000 totaled $7,125,000, a
decrease of 11% from the same period of fiscal 1999. For the quarter ended June
30, 2000, depreciation decreased $442,000, or 17%. Depreciation decreased as a
result of a suspension of capital expenditures during fiscal 1999 due to
industry conditions.

Total operating costs for the first nine months of fiscal 2000 were
$23,890,000, a decrease of 8%, from the same period of fiscal 1999 due to the
factors described above. For the quarter ended June 30, 2000, total operating
costs decreased 10% from the same period of the prior fiscal year. The 36%
decrease of revenues as compared to the 8% decrease of total operating costs
for the nine months ended June 30, 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 21%
primarily as a result of establishing a deferred tax valuation allowance in the
current year.

LIQUIDITY AND CAPITAL RESOURCES

Cash Flows

Net cash provided by operating activities of $907,000 for the nine months ended
June 30, 2000 primarily reflects the net loss offset by depreciation and
changes in working capital components. The decreases in deferred income taxes
are 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 nine months ended June 30, 2000
represents management of short-term investments and severely limited capital
expenditures.

The cash flows provided by financing activities for the nine months ended June
30, 2000 represent the proceeds from the exercise of a stock option.

                                      -9-
<PAGE>   10


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.
During the fourth quarter of fiscal 2000, the Company will purchase additional
channel capacity that has become available at a significant discount. The
Company maintains 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 cover- age of the damages, if any,
which may be assessed against the Company in such litiga- tion. 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 signifi- cantly 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 June 30, 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

Part II.  OTHER INFORMATION


Item 6.  Exhibits and Reports on Form 8-K

                  (a)      Exhibits
                           The information required by this Item 6(a) is set
                           forth in the Index to Exhibits accompanying this
                           quarterly report and is Incorporated herein by
                           reference.

                  (b)      No reports on Form 8-K were filed by the Company
                           during the quarter ended June 30, 2000.








                                      -11-



<PAGE>   12
                                   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:       July 28, 2000
            -------------



                                      -12-


<PAGE>   13


                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>

EXHIBIT
NUMBER                        DESCRIPTION
-------                       -----------
<S>                           <C>
27                            Financial Data Schedule
</TABLE>