<PAGE>   1

                                    FORM 10-Q

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549


[X]            QUARTERLY REPORT PURSUANT TO SECTION 13 or 15(D) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

For the Quarterly Period Ended     June 30, 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              0-21682
                      ---------------------------------

                                  SPARTA, Inc.
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)

           Delaware                                                63-0775889
--------------------------------------------------------------------------------
(State or other jurisdiction of                                (I.R.S. Employer)
 incorporation or organization)

       23041 Avenida de la Carlota, Suite 325, Laguna Hills, CA 92653-1595
--------------------------------------------------------------------------------
             (Address of principal executive offices)           (Zip Code)

                                 (949) 768-8161
--------------------------------------------------------------------------------
              (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 or 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
     -----           -----

As of July 5, 1998, the registrant had 5,756,473 shares of common stock, $.01
par value per share, issued and outstanding.

<PAGE>   2

                                  SPARTA, Inc.

               QUARTERLY REPORT FOR THE PERIOD ENDED JUNE 30, 1998

                                      INDEX


PART I  FINANCIAL STATEMENTS

ITEM 1  Quarterly Financial Statements

        Statements of Income for the Six Months Ended June 30, 1998 and June 30,
        1997 (Unaudited)

        Balance Sheets as of June 30, 1998 and December 31, 1997 (Unaudited)

        Statement of Cash Flows for the Six Months Ended June 30, 1998 and June
        30, 1997 (Unaudited)

        Notes to Consolidated Financial Statements (Unaudited)

ITEM 2  Management's Discussion and Analysis of Financial Condition and Results
        of Operations

PART II OTHER INFORMATION

SIGNATURE

EXHIBIT 11     Computations of Earnings per Share

<PAGE>   3

                                     PART I


                              FINANCIAL STATEMENTS

<PAGE>   4

CONSOLIDATED STATEMENT OF INCOME
          (UNAUDITED)

ITEM 1.  FINANCIAL STATEMENTS
---------------------------------

<TABLE>
<CAPTION>
                                       THREE MONTHS ENDED JUNE 30       SIX MONTHS ENDED JUNE 30
                                       ---------------------------     ---------------------------
                                          1998            1997            1998            1997
                                       -----------     -----------     -----------     -----------
<S>                                    <C>             <C>             <C>             <C>        
SALES                                  $23,650,000     $21,277,000     $46,594,000     $40,111,000
                                       -----------     -----------     -----------     -----------
COSTS AND EXPENSES:

  Labor costs and related benefits      12,096,000      10,850,000      24,537,000      21,026,000

  Subcontractor & other costs            6,717,000       5,624,000      12,582,000      10,150,000

  Facility costs                         1,823,000       1,665,000       3,636,000       3,537,000

  Travel and other                       1,044,000         938,000       1,684,000       1,740,000

  Interest expense, net                    116,000          73,000         198,000         108,000
                                       -----------     -----------     -----------     -----------
                                        21,796,000      19,150,000      42,637,000      36,561,000
                                       -----------     -----------     -----------     -----------
INCOME BEFORE PROVISION FOR
  TAXES ON INCOME                        1,854,000       2,127,000       3,957,000       3,550,000

PROVISION FOR TAXES ON INCOME              779,000         893,000       1,662,000       1,491,000
                                       -----------     -----------     -----------     -----------
NET INCOME                             $ 1,075,000     $ 1,234,000     $ 2,295,000     $ 2,059,000
                                       ===========     ===========     ===========     ===========
BASIC EARNINGS PER SHARE               $      0.13     $      0.17     $      0.26     $      0.26
                                       ===========     ===========     ===========     ===========
DILUTED EARNINGS PER SHARE             $      0.12     $      0.16     $      0.25     $      0.25
                                       ===========     ===========     ===========     ===========
</TABLE>

* EARNINGS PER SHARE AMOUNTS PRESENTED FOR PRIOR YEARS HAVE BEEN RESTATED IN
  ACCORDANCE WITH STATEMENT OF FINANCIAL ACCOUNTING STANDARDS NO. 128, "EARNINGS
  PER SHARE".

     The accompanying notes are an integral part of the financial statements

<PAGE>   5

CONSOLIDATED BALANCE STATEMENT
         (UNAUDITED)

<TABLE>
<CAPTION>
                                                        JUNE 30            DECEMBER 31,
                                                          1998                 1997
                                                      ------------         ------------
                                                      (Unaudited)           (Audited)
<S>                                                   <C>                  <C>         
ASSETS

CURRENT ASSETS
  Cash                                                $    244,000         $    198,000
  Accounts receivable                                   20,180,000           23,557,000
  Prepaid expenses                                         572,000              448,000
                                                      ------------         ------------
    TOTAL CURRENT ASSETS                                20,996,000           24,203,000

  Equipment and improvements, net                        8,406,000            7,321,000
  Other assets                                           1,956,000            1,685,000
                                                      ------------         ------------
    TOTAL ASSETS                                      $ 31,358,000         $ 33,209,000
                                                      ============         ============


LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT LIABILITIES
  Accrued compensation                                $  3,655,000         $  5,723,000
  Accounts payable and other accrued expenses              722,000            3,005,000
  Current portion of notes payable                         440,000              477,000
  Income tax payable                                            --              199,000
  Deferred income taxes                                  2,422,000            2,446,000
                                                      ------------         ------------
    TOTAL CURRENT LIABILITIES                            7,239,000           11,850,000

NOTES PAYABLE                                            2,925,000            2,658,000

SUBORDINATED NOTES PAYABLE                                 434,000              646,000

DEFERRED INCOME TAXES                                    1,111,000            1,677,000

Commitments and contingencies

REDEEMABLE PREFERRED STOCK
  Preferred stock, $.01 par value; 2,000,000
  shares authorized; 569,039 and 569,039
  shares issued and outstanding                          4,734,000            3,926,000

STOCKHOLDERS' EQUITY
  Common stock, $.01 par value, 25,000,000
  shares authorized; 13,606,953 and 13,070,700
  shares issued                                            136,000              131,000
  Additional paid-in capital                            29,754,000           26,340,000
  Retained earnings                                     26,640,000           25,152,000
  Treasury stock                                       (41,615,000)         (39,171,000)
                                                      ------------         ------------
    TOTAL STOCKHOLDERS' EQUITY                          14,915,000           12,452,000
                                                      ------------         ------------
TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY            $ 31,358,000         $ 33,209,000
                                                      ============         ============
</TABLE>

     The accompanying notes are an integral part of the financial statements

<PAGE>   6

CONSOLIDATED STATEMENT OF CASH FLOWS
           (UNAUDITED)

<TABLE>
<CAPTION>
                                                            SIX MONTHS ENDED JUNE 30
                                                          -----------------------------
                                                              1998              1997
                                                          -----------       -----------
<S>                                                       <C>               <C>        
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net Income                                              $ 2,295,000       $ 2,059,000
  Adjustments to reconcile net income to net
    cash provided by operating activities:
      Depreciation and amortization                           751,000           787,000
      Loss on sale of equipment                                 5,000           105,000
      Employee compensation paid in stock                   1,969,000         1,283,000
      Changes in assets and liabilities:
        Accounts receivable                                 2,964,000         2,040,000
        Prepaid expenses                                     (125,000)          (92,000)
        Other assets                                          141,000          (274,000)
        Accrued compensation                               (2,068,000)         (142,000)
        Accounts payable and other accrued expense         (2,283,000)       (1,144,000)
        Income taxes payable                                 (223,000)         (758,000)
        Deferred income taxes                                (566,000)         (564,000)
      Tax benefit relating to stock plan                      357,000            59,000
                                                          -----------       -----------
          NET CASH PROVIDED BY OPERATING ACTIVITIES         3,217,000         3,359,000
                                                          -----------       -----------

CASH FLOWS FROM INVESTING ACTIVITIES:
    Capital expenditures                                    1,840,000        (1,308,000)
                                                          -----------       -----------
          NET CASH USED IN INVESTING ACTIVITIES             1,840,000        (1,308,000)
                                                          -----------       -----------

CASH FLOWS FROM FINANCING ACTIVITIES:
  Proceeds from issuance of stock                           1,094,000           955,000
  Cash purchases of treasury stock                         (2,033,000)       (2,387,000)
  Net (repayments) proceeds line-of-credit agreement          268,000          (228,000)
  Principal payments on debt                                 (660,000)         (360,000)
                                                          -----------       -----------
          NET CASH USED IN FINANCING ACTIVITIES            (1,331,000)       (2,020,000)
                                                          -----------       -----------

NET DECREASE IN CASH                                           46,000            31,000
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD              198,000           151,000
                                                          -----------       -----------
CASH AND CASH EQUIVALENTS AT END OF PERIOD                $   244,000       $   182,000
                                                          ===========       ===========

SUPPLEMENTAL DISCLOSURES OF CASH FLOW INFORMATION:
  Cash paid during the period for:
    Interest                                              $   202,000       $   108,000
                                                          ===========       ===========
    Income taxes                                          $ 2,451,000       $ 2,762,000
                                                          ===========       ===========
</TABLE>

     The accompanying notes are an integral part of the financial statements

<PAGE>   7


                                  SPARTA, INC.

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                   ------------------------------------------
                                   (Unaudited)


NOTE A - BASIS OF PRESENTATION
------------------------------

The accompanying financial information has been prepared in accordance with the
instructions to Form 10-Q and therefore does not necessarily include all
information and footnotes necessary for a fair presentation of financial
position, results of operations and cash flows in conformity with generally
accepted accounting principles.

The Company's fiscal year is the 52 or 53 week period ending on the Friday
closest to December 31. The Company's last fiscal year ended on January 2, 1998;
and, its first quarter ended July 5, 1998 and corresponding second quarter last
year on July 4, 1997. To aid the reader of the financial statements, the year
end has been presented as December 31, 1997 and the quarters and six months
ended June 30, 1997 and June 30, 1998.

In the opinion of management, the unaudited financial information for the
six-month periods ended June 30, 1998 and June 30, 1997 reflects all adjustments
(which include only normal, recurring adjustments) necessary for a fair
presentation thereof.

NOTE B - RECEIVABLES
--------------------

Unbilled accounts receivable include $1,874,000 of costs incurred on projects
for which the Company has been requested by the customer to begin work under a
new contract or extend work under a present contract, but for which final
contract negotiations or formal contracts or contract modifications have not
been executed at June 30, 1998.

NOTE C - INCOME TAXES
---------------------

Income taxes for interim periods are computed using the estimated annual
effective rate method.

<PAGE>   8

ITEM 2.   MANAGEMENT'S DISCUSSION AND ANALYSIS
----------------------------------------------
OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS
------------------------------------------------


The Management Discussion and Analysis of Financial Condition and Results of
Operation contains forward-looking statements that involve risks and
uncertainties. The Company's actual results may differ significantly from
projections contained in forward-looking statements. For a more complete
discussion of the factors which could cause such a difference, the Company's
Form 10-K for the year ended December 31, 1997, should be consulted.

The following table sets forth, for the periods indicated, selected financial
results from the Company's continuing operations and audited Financial
Statements.

RESULTS OF OPERATIONS

<TABLE>
<CAPTION>
                                     Three months ended            Six months ended 
                                          June 30,                      June 30,
                                  -------------------------    ------------------------
                                     1998           1997          1998          1997
                                  ----------     ----------    ----------    ----------
<S>                               <C>            <C>           <C>           <C>       
  Sales                           23,650,000     21,277,000    46,594,000    40,111,000
  Gross profit (1)                 2,093,000      2,416,000     4,312,000     3,952,000
  Gross profit as a % of costs          9.71%         12.81%        10.20%        10.93%
  Net income (2)                   1,075,000      1,234,000     2,295,000     2,059,000
  Number of staff                        679            575           679           575
</TABLE>

<TABLE>
<CAPTION>
                                                               Balance at
                                                ----------------------------------------
                                                  June 30,    December 31,    June 30,
                                                    1998         1997           1997
                                                ------------ -------------  ------------
<S>      <C>                                     <C>           <C>           <C>       
  Funded 12 month backlog                        35,900,000    29,900,000    41,000,000
  Total 12 month contract backlog                88,900,000    93,200,000    86,800,000
  Stockholders equity                            14,915,000    12,452,000    11,469,000
  Equity per share (3)                                 2.36          1.89          1.80
  Stock repurchase notes                            874,000     1,123,000     1,781,000
  Line of credit                                  2,925,000     2,658,000       233,000
  Number in days sales in receivables                    80            93            81
  Current ratio                                         2.9           2.1           2.0
</TABLE>

(1)   The Company defines gross profits as sales less costs and expenses
      excluding interest costs and certain expenses which cannot be billed to
      its government customers.
(2)   Prior to adjustments for interest and accretion on stock - See Exhibit 11.
(3)   Equity per share based on weighted shares of common stock outstanding for
      period ending, including weighted shares of preferred stock outstanding.

REVENUES

The Company's contract revenues for the second quarter were up 11.2% from the
corresponding three month period in 1997. Second quarter sales of $23,650,000
were the highest quarterly total in the Company's history. Profitability for the
three month period ended June 30, 1998 was down 13.4% when compared to the
corresponding period of 1997. Profitability as a percent of costs decreased from
12.8% to 9.7% for the corresponding period in 1998. Borrowings against the
Company's line of credit totaled $2,925,000 as of the end of the 2nd quarter
compared to a borrowing level of $233,000 at the end of the corresponding period
in 1997. This is primarily due to the high capital spending and independent
research and development (IR&D) spending in the first two quarters of this year.
The Company has been successful in reducing its days sales from 97 days at March
31, 1998 to 80 days at June 30, 1998. The Company believes that reducing
spending for capital and IR&D items as well as improvement in days sales will
contribute to a reduction in borrowing requirements during the second half of
the year.

<PAGE>   9

ANNUALIZED BACKLOG

During the second quarter, the Company had one new competitive win - the
Integrated Data and Systems Operation won the re-compete of the Army SSDC's
Defense Systems Mission Analysis contract. This is a $9,300,000 contract over
five years. The company had two major losses during the second quarter. One was
a bid to Lockheed-Martin by Advance Materials Products Operations for JASSM
parts. This was a $9,600,000 bid over seven years. The other loss was by the
Integrated Data and Systems Operation on an Army program named CIMS. This was a
subcontract bid to Kottman, Inc. for $15,750,000 over seven years. Funding
increments on existing contracts were down 12.4% from the same period last year.
The Company's funded backlog at the end of the second quarter was $35,900,000 as
compared to $41,000,000 for the same period last year.

Annualized contract backlog decreased 4.6% in the first two quarters from the
backlog starting the year. Backlog went from $93,200,000 to start the year to
$88,900,000 at the end of the second quarter. The Company plans to submit many
proposals in the next two quarters as the opportunity backlog is strong.

LIQUIDITY AND CAPITAL RESOURCES

The Company's primary sources of liquidity are funds provided by operations and
the bank line of credit. The Company's line of credit limit is $12,000,000.
Borrowings under the line of credit at June 30, 1998 totaled $2,925,000. Days
sales outstanding decreased to 80 days at June 30, 1998, from 97 days at March
31, 1998, and from 81 days at June 30, 1997. The Company continues to actively
monitor receivables with emphasis placed on collection activities. The Company's
debt-to-equity ratio, as defined by the bank, was 0.5 at June 30, 1998 versus
0.8 at December 31, 1997 and 0.6 at June 30, 1997. All capital expenditures were
financed through operating funds and the revolving line of credit. The Company's
cash flow from operations plus borrowing under its line of credit are expected
to provide sufficient funds for the Company's operations, common stock
repurchases, capital expenditures, and future long-term debt requirements.

STOCKHOLDER EQUITY

The Company increased stockholder's equity from $12,452,000 at the end of 1997
to $14,915,000 at June 30, 1998. The Company's strong earnings and net proceeds
from the sale and repurchase of stock have accounted for this increase. The
Company is now repurchasing all the stock from terminating employees and intends
to continue to do so for the rest of the year.

STOCK PURCHASE AGREEMENT

In November, 1994, the Company entered into a Stock Purchase Agreement (the
"Agreement") with Science Applications International Corporation ("SAIC"), under
which SAIC was obligated to buy, during the first year of the Agreement, shares
of the Company's Preferred Stock with an aggregate price of $1,200,000. Under
the Agreement, SAIC also has the option, but not the obligation, to buy
additional shares of Preferred Stock, provided that SAIC's total purchases
during any quarter may not exceed $600,000 and provided further, that the total
number of shares of Preferred Stock purchases during any quarter may not exceed
the total number of shares of Common Stock offered to the Company for repurchase
by the Company's existing stockholders. The purchase price for all shares
purchased under the Agreement by SAIC is equal to the then current Formula Price
applicable to the Company's Common Stock. The Agreement grants SAIC the option
to require the Company to repurchase all of the Preferred Stock held by SAIC at
the Formula Price at time of option exercise. In the event the option is
exercised, the Company may issue SAIC a subordinated note bearing an interest
rate equal to the lesser of prime or 10%. SAIC suspended its purchase of Company
preferred stock in the last quarter of 1996 and has not purchased any stock
since. The total purchase as of June 30, 1998 of $2,400,000 (569,039 shares) of
Company Preferred Stock represents 9.08% of the Company's total outstanding
stock. Through June 30, 1998 accretion of Preferred Stock was $2,334,000.

EFFECTS OF FEDERAL FUNDING FOR DEFENSE PROGRAMS

The Company continues to have over 90% of its contracts with the Department of
Defense. The Company anticipates little or no effect on its anticipated sales
for 1998 as a result of the outcome of the November, 1998 federal elections for
the Senate and House of Representatives. However, sales in its government
business areas for 1999 and subsequent years could be impacted by this election
and the yet to be resolved federal budget for Government Fiscal Year 1999.

<PAGE>   10

PART II   OTHER INFORMATION

ITEM 1    LEGAL PROCEEDINGS

The Company has no investigations, claims, and lawsuits arising out of its
business, nor any known to be pending.

ITEM 2    CHANGES IN SECURITIES

Not Applicable

ITEM 3    DEFAULTS UPON SENIOR SECURITIES

Not Applicable

ITEM 4    SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

The Company's Annual Meeting will be held on May 1, 1998 at which time proxies
and shareholders present voted on and approved the 1997 Stock Plan, the Amended
and Restated Certificate of Incorporation, the Directors and the continuation of
Price Waterhouse as auditor.

ITEM 5    OTHER MATERIALLY IMPORTANT EVENTS

Not Applicable

ITEM 6    EXHIBITS AND REPORTS ON FORM 8-K

(a)  Exhibits
     --------
       11      Statement re: Computation of Per Share Earnings
       27      Financial Data Schedule

(b)  Reports on Form 8-K
     -------------------

No report(s) on Form 8-K were filed by the Company during the fiscal quarter for
which this report is filed.

<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.



                                                   SPARTA, INC.


Date:   August 17, 1998                 /s/ B. Warren Knudson
                                        ----------------------------------------
                                        B. Warren Knudson Vice President and
                                        Chief Financial Officer (Principal
                                        Finance and Accounting Officer)

<PAGE>   12

                                  EXHIBIT INDEX

                                  SPARTA, INC.

                           QUARTER ENDED JUNE 30, 1998




<TABLE>
<CAPTION>
Exhibit                                                                         Sequential
  No.             Description of Exhibits                                        Page No.
  ---             -----------------------                                        --------
<C>               <S>                                                           <C>
   11             Statement re:  Computation of Per Share Earnings
   27             Financial Data Schedule
</TABLE>