<PAGE>
 
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                                        
                                  FORM 10-QSB


[X]  QUARTERLY REPORT UNDER SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT
     OF 1934
     For the quarterly period ended June 30, 1998



[_]  TRANSITION REPORT UNDER SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT
     OF 1934
     For the transition period from __________ to __________



                        Commission file number: 0-28560


                            RESEARCH ENGINEERS, INC.
       (Exact name of small business issuer as specified in its charter)


          Delaware                                       22-2356861
(State or other jurisdiction of              (IRS. Employer Identification No.)
        incorporation)


                            22700 SAVI RANCH PARKWAY
                         YORBA LINDA, CALIFORNIA 92887
                    (Address of principal executive offices)

                                 (714) 974-2500
              (Registrant's telephone number, including area code)


Check whether the issuer:  (1) filed all reports required to be filed by Section
13 or 15(d) of the Exchange Act during the past 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 [_]


The number of shares outstanding of the registrant's only class of Common Stock,
$.01 par value, was 5,680,710 on July 27, 1998.
<PAGE>
 
PART I -- FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS

                   RESEARCH ENGINEERS, INC. AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEET
                                 JUNE 30, 1998
                                  (Unaudited)
               (In thousands, except share and per share amounts)
<TABLE>
<CAPTION>
 
                                   Assets
<S>                                                                     <C> 
Current assets:
 Cash and cash equivalents                                              $ 1,069
 Short-term investments                                                   1,620
 Accounts receivable (net of allowance for doubtful accounts of $343)     1,835
 Deferred income taxes                                                      688
 Notes and related party loans receivable                                   150
 Prepaid expenses and other current assets                                  440
                                                                        -------
 
      Total current assets                                                5,802
 
Property, plant and equipment, net                                        3,182
Goodwill (net of accumulated amortization of $572)                        1,016
Other assets                                                                900
                                                                        -------
 
                                                                        $10,900
                                                                        =======
 
                      Liabilities and Stockholders' Equity
Current liabilities:
 Current portion of long-term bank debt                                 $   127
 Accounts payable                                                           278
 Accrued expenses                                                           439
 Income taxes payable                                                       378
 Deferred maintenance revenue                                               894
 Other                                                                       30
                                                                        -------
 
      Total current liabilities                                           2,146
 
Long-term bank debt                                                       1,817
Deferred income taxes                                                        72
                                                                        -------
 
      Total liabilities                                                   4,035
                                                                        -------
 
Stockholders' equity:
 Preferred stock, par value $.01.  Authorized 5,000,000 shares; issued 
  and outstanding none                                                        -
 Common stock, par value $.01.  Authorized 20,000,000 shares; issued 
  and outstanding 5,680,710 shares                                           57
 Additional paid-in capital                                               6,602
 Retained earnings                                                          515
 Accumulated other comprehensive income                                    (309)
                                                                        -------
 
      Total stockholders' equity                                          6,865
                                                                        -------
                                                                        $10,900
                                                                        =======
</TABLE> 
 
See accompanying notes to consolidated financial statements.

                                       2
<PAGE>
 
                   RESEARCH ENGINEERS, INC. AND SUBSIDIARIES
                     CONSOLIDATED STATEMENTS OF OPERATIONS
                                  (Unaudited)
               (In thousands, except share and per share amounts)

<TABLE>
<CAPTION>
                                        Three Months       Three Months  
                                            Ended              Ended     
                                        June 30, 1998      June 30, 1997 
                                        -------------      ------------- 
<S>                                         <C>                <C>      
Net revenues:                                                            
 Product sales                              $   1,652          $   2,369    
 Maintenance and support                          454                426    
                                            ---------          ---------    
                                                                            
      Total net revenues                        2,106              2,795    
                                                                            
Cost of revenues                                  248                242    
                                            ---------          ---------    
                                                                            
      Gross profit                              1,858              2,553    
                                            ---------          ---------    
                                                                            
Operating expenses:                                                         
 Selling, general and administrative            1,411              2,128    
 Research and development                         615                450    
                                            ---------          ---------    
                                                                            
      Total operating expenses                  2,026              2,578    
                                            ---------          ---------    
                                                                            
      Operating loss                             (168)               (25)   
                                            ---------          ---------    
                                                                            
Other (income)/expense:                                                     
 Interest, net                                     15                (19)   
 Other                                            (16)               (17)   
                                            ---------          ---------    
                                                                            
      Total other income                           (1)               (36)   
                                            ---------          ---------    
                                                                            
(Loss)/income before income taxes                (167)                11    
                                                                            
Income tax benefit                                (43)                (5)   
                                            ---------          ---------    
                                                                            
      Net (loss)/income                     $    (124)         $      16    
                                            =========          =========    
                                                                            
Net (loss)/income per common share:                                         
         Basic                              $   (0.02)         $    0.00    
                                            =========          =========    
         Diluted                            $   (0.02)         $    0.00    
                                            =========          =========    
                                                                            
Common shares used in computing net                                         
 (loss)/income per common share:                                            
         Basic                              5,679,710          5,701,000    
                                            =========          =========    
         Diluted                            5,679,710          5,756,885    
                                            =========          =========     
</TABLE> 
 
 
See accompanying notes to consolidated financial statements.

                                       3
<PAGE>
 
                   RESEARCH ENGINEERS, INC. AND SUBSIDIARIES
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                                  (Unaudited)
                                 (In thousands)
<TABLE>
<CAPTION>
                                                                               Three Months         Three Months 
                                                                                   Ended                Ended
                                                                               June 30, 1998        June 30, 1997
                                                                               -------------        -------------
<S>                                                                            <C>                  <C> 
Cash flows from operating activities:
 Net (loss)/income                                                                    $ (124)             $    16
 Adjustments to reconcile net (loss)/income to net cash used in operating
  activities:
    Depreciation and amortization                                                        235                  178              
    Deferred income taxes                                                                (77)                 (56)              
    Gain on investments                                                                  (21)                  (1)              
    Changes in operating assets and liabilities:                                                                               
     Accounts receivable                                                                 367                  100              
     Notes and related party loans receivable                                            (44)                  (1)              
     Prepaid expenses and other current assets                                           (45)                  23              
     Other assets                                                                        (51)                (407)              
     Accounts payable, accrued expenses and other current liabilities                   (121)                (185)              
     Deferred maintenance revenue                                                       (131)                 146              
     Income taxes payable                                                                (41)                 (23)              
     Other long-term liabilities                                                           -                   (9)              
                                                                                      ------              -------
 
          Net cash used in operating activities                                          (53)                (219)
                                                                                      ------              -------
 
Cash flows from investing activities:
 Purchase of property, plant and equipment                                              (209)                 (90)
 Purchase of short-term investments                                                     (365)              (2,933)
 Sale of short-term investments                                                          349                1,383
                                                                                      ------              -------
 
          Net cash used in investing activities                                         (225)              (1,640)
                                                                                      ------              -------
 
Cash flows from financing activities:
 Proceeds from bank debt                                                                  58                    -
 Repayment of bank debt                                                                  (25)                 (24)
 Common stock issuance from exercise of options                                            8                    -
                                                                                      ------              -------
 
          Net cash provided (used in) by financing activities                             41                  (24)
                                                                                      ------              -------
 
 Effect of exchange rate changes on cash and cash equivalents                            (34)                 (26)
                                                                                      ------              -------
 
          Decrease in cash and cash equivalents                                         (271)              (1,909)
 
 
Cash and cash equivalents, beginning of period                                         1,340                2,579
                                                                                      ------              -------

Cash and cash equivalents, end of period                                              $1,069              $   670
                                                                                      ======              ======= 
</TABLE> 
 
See accompanying notes to consolidated financial statements.

                                       4
<PAGE>
 
                   RESEARCH ENGINEERS, INC. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                 JUNE 30, 1998
                                  (Unaudited)


1.  BASIS OF PRESENTATION

    The consolidated financial statements include the accounts of Research
    Engineers, Inc. (the "Company") and its wholly-owned subsidiaries. These
    consolidated financial statements have been prepared by the Company, without
    audit, and include all adjustments which are, in the opinion of management,
    necessary for a fair presentation of the results of operations for the three
    months ended June 30, 1998 and 1997, the financial position at June 30,
    1998, and the cash flows for the three months ended June 30, 1998 and 1997,
    pursuant to the rules and regulations of the Securities and Exchange
    Commission. Accordingly, they do not include all of the information and
    footnotes required by generally accepted accounting principles for complete
    financial statements. Results of operations for the three months ended June
    30, 1998 are not necessarily indicative of the results to be expected for
    the full year ended March 31, 1999.


2.  USE OF ESTIMATES

    The preparation of financial statements in conformity with generally
    accepted accounting principles requires management to make estimates and
    assumptions that affect the amounts reported in the consolidated financial
    statements and accompanying notes. Actual results could differ from those
    estimates.


3.  RECLASSIFICATIONS

    Certain prior quarter amounts have been reclassified to conform to the
    current quarter presentation.


4.  SOFTWARE REVENUE RECOGNITION


    In October 1997, the American Institute of Certified Public Accountants
    ("AICPA") issued Statement of Position ("SOP") 97-2, Software Revenue
    Recognition, which supercedes SOP 91-1. SOP 97-2 distinguishes between
    significant and insignificant vendor obligations as a basis for recording
    revenue with a requirement that each element of a software licensing
    arrangement be separately identified and accounted for based on relative
    fair values of each element. The Company adopted SOP 97-2 in the first
    quarter of fiscal 1999, the implementation of which resulted in no material
    changes to the Company's previous practice.


5.  COMPREHENSIVE INCOME


    As of April 1, 1998, the Company adopted Statement of Financial Accounting
    Standards ("SFAS") No. 130, Reporting Comprehensive Income. SFAS No. 130
    establishes new rules for the reporting and display of comprehensive income
    and its components; however, the adoption of this statement had no impact on
    the Company's reported net income or stockholders' equity. SFAS No. 130
    requires unrealized gains or losses on the Company's available-for-sale
    investments and foreign currency translation adjustments, which prior to
    adoption were reported separately in stockholders' equity, to be included in
    other comprehensive income. The prior year Consolidated Statement of
    Stockholders' Equity will be reclassified at year-end fiscal 1999 to conform
    to the requirements of SFAS No. 130. During the first quarter of fiscal 1999
    and 1998, total comprehensive (loss)/income was ($282,000) and $3,000,
    respectively.

                                       5
<PAGE>
 
6.  NET (LOSS)/INCOME PER SHARE


    In December 1997, the Financial Accounting Standards Board ("FASB") issued
    SFAS No. 128, Earnings per Share ("EPS"). SFAS No. 128 replaced the
    calculation of primary and fully diluted EPS with basic and diluted EPS.
    Unlike primary EPS, basic EPS excludes any dilutive effects of common stock
    equivalents, such as options and warrants. Diluted EPS is very similar to
    the previously reported fully diluted EPS. All EPS amounts for all periods
    have been restated to conform to the SFAS No. 128 requirements.

    The following table illustrates the computation of basic and diluted net
    income/(loss) per share (in thousands):

<TABLE>
<CAPTION>
                                                                     Three Months        Three Months
                                                                        Ended               Ended
                                                                    June 30, 1998       June 30, 1997
                                                                    -------------       -------------
<S>                                                                     <C>                  <C>
Numerator:                                                          
Numerator for basic and diluted net (loss)/income per share            
 net (loss)/income                                                      $ (124)              $   16                        
                                                                        ======               ======
Denominator:                                                                                  
Denominator for basic net (loss)/income per share - average              
 number of common shares outstanding during the period                   5,680                5,701
Incremental common shares attributable to exercise of                                              
 outstanding options                                                         -                   56                       
                                                                        ------               ------
Denominator for diluted net (loss)/income per share                      5,680                5,757
                                                                        ======               ======
                                                                                              
Basic net (loss)/income per share                                       $(0.02)              $ 0.00
                                                                        ======               ======
Diluted net (loss)/income per share                                     $(0.02)              $ 0.00
                                                                        ======               ======
</TABLE>


    The computation of diluted loss per share for the three-month period ended
    June 30, 1998 excluded the effect of 248,000 incremental common shares
    attributable to the exercise of outstanding common stock options because
    their effect was antidilutive.

    Warrants issued to the underwriters as part of the Company's initial public
    offering to purchase 130,000 shares of common stock at $6.00 per share were
    outstanding during the three months ended June 30, 1998 and 1997 but were
    not included in the computation of diluted EPS because the warrants'
    exercise price was greater than the average market price of the common
    shares and, therefore, the effect would be antidilutive.

                                       6
<PAGE>
 
ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OR PLAN OF OPERATION

GENERAL

Research Engineers, Inc. (the "Company") is a leading provider of technically
sophisticated stand-alone and network-based engineering software products that
provide fully-integrated easy-to-use design automation and analysis solutions
for use by engineering analysis and design professionals worldwide.  The
Company's comprehensive line of Windows-based engineering software products
includes STAAD-III, the Company's flagship structural analysis and design
software; STAAD/Pro, the first comprehensive structural design office solution;
as well as mechanical, civil and process/piping engineering products.  The
Company's software products assist engineers in performing a myriad of mission-
critical engineering tasks, including analysis and design of industrial,
commercial, transportation and utility structures, pipelines, machinery,
automotive and aerospace products, and survey, contour and digital terrain
modeling.

The following discussion and analysis addresses the results of the Company's
operations for the three months ended June 30, 1998, as compared to the
Company's results of operations for the three months ended June 30, 1997.


RESULTS OF OPERATIONS FOR THE THREE MONTHS ENDED JUNE 30, 1998 AND 1997

Net revenues - Net revenues for the quarter ended June 30, 1998 decreased by
$689,000 (25%) to $2,106,000, as compared to $2,795,000 for the quarter ended
June 30, 1997. This decrease in net revenues was primarily attributable to the
decline in economic conditions in Southeast Asia that started during the latter
part of fiscal 1998. Revenues to Southeast Asia during the first quarter of
fiscal 1998 represented 31% of the company's total revenues, compared to only 9%
during the first quarter of fiscal 1999.

Revenues are derived primarily from sales of the Company's engineering software
products and, to a lesser extent, from sales of software maintenance contracts
relating to its products. Software product revenues are recognized upon
shipment. In accordance with the American Institute of Certified Public
Accountants ("AICPA") Statement of Position ("SOP") 97-2, Software Revenue
Recognition, issued in 1997, which supercedes SOP 91-1, product maintenance
revenues are amortized over the length of the maintenance contract, which is
usually twelve months.  The implementation of SOP 97-2 did not result in any
material changes from the Company's previous practice.

International net revenues as a percentage of total revenues for the quarter
ended June 30, 1998 decreased to 42%, down from 61% for the quarter ended June
30, 1997. The decrease in international revenues for the period was primarily
the result of the decline in economic conditions in Southeast Asia that started
during the latter part of fiscal 1998. The Company expects this trend to
continue into the next several quarters, and therefore, remains cautious about
its short-term Southeast Asia prospects. The Company's domestic revenues are
denominated in U.S. Dollars, while revenues and expenses for the Company's
foreign subsidiaries and sales offices are usually recorded in the applicable
foreign currency and translated with any applicable foreign exchange
adjustments.  There were no foreign exchange gains or losses that were material
to the Company's financial results during the three-month periods ended June 30,
1998 and 1997.

Gross Profit - Gross profit decreased by $695,000 (27%) to $1,858,000 in the
quarter ended June 30, 1998 as compared to $2,553,000 for the quarter ended June
30, 1997. This decrease was primarily due to decreased sales volume.  The slight
increase in cost of revenues resulted from an increase in capitalized software
amortization which fluctuates independent of revenue.

Selling, general and administrative expense - Selling, general and
administrative expense decreased by $717,000 (34%) to $1,411,000 for the quarter
ended June 30, 1998 as compared to $2,128,000 for the quarter ended June 30,
1997, and decreased as a percentage of net revenues to 67% from 76% in the
comparable quarter of the prior year. The majority of the fluctuation is due to
a decrease in sales commissions being paid associated with declining net
revenues in the Southeast Asia markets, which are among the Company's highest
commission rate markets. General and administrative expenses in the three-

                                       7
<PAGE>
 
month period decreased due to a one-time charge for severance paid to a former
QSE (Bristol) Limited employee during the first quarter of fiscal 1998 which
also resulted in a decrease in salaries, combined with a decrease in royalties
paid to outside companies due to the expiration of certain royalty agreements.

Research and development expense - Research and development expense increased by
$165,000 (37%) to $615,000 in the quarter ended June 30, 1998 as compared to
$450,000 for the quarter ended June 30, 1997, and increased as a percentage of
net revenues to 29% from 16% in the comparable quarter of the prior year. The
increases in research and development expense are primarily due to the addition
of research and development personnel since the first quarter of fiscal 1998, as
well as additional costs paid to outside consultants for research and
development projects.

Other (income) expense - Net interest (income) expense decreased by $35,000 to
($1,000) in the quarter ended June 30, 1998 as compared to ($36,000) for the
quarter ended June 30, 1997. The decrease results from a decline in the
Company's short-term investment balances since the first quarter of fiscal 1998
and the resulting decrease in interest income.

Income taxes - Income tax benefit increased by $38,000 to $43,000 in the quarter
ended June 30, 1998 as compared to $5,000 for the quarter ended June 30, 1997.
This increase in income tax benefit is primarily due to a pretax loss in the
United States and Singapore for the three months ended June 30, 1998 and the
related tax benefit for the net operating loss that was recorded.  The Company
increased its deferred tax asset during the current quarter by $77,000 and
believes that this asset will be realizable against future earnings.

LIQUIDITY AND CAPITAL RESOURCES

Certain statements contained in this report, including those contained in
"Results of Operations for the Three Months Ended June 30, 1998 and 1997" and
"Liquidity and Capital Resources" are "forward-looking statements" that involve
risks and uncertainties.  The actual future results of the Company could differ
materially from those statements.  Factors that could cause or contribute to
such differences include, but are not limited to, those discussed in this
report, uncertainties regarding market acceptance of new products and product
enhancements, delays in the introduction of new products, and risks associated
with managing the Company's growth, as well as those factors discussed in the
Company's Form 10-KSB for the fiscal year ended March 31, 1998 which was filed
with the Securities and Exchange Commission on June 29, 1998 and the risks
described in the "Outlook" section therein.

The Company currently finances its operations (including capital expenditures)
primarily through cash flows from operations as well as its cash and short-term
investment balances.

The Company's principal sources of liquidity at June 30, 1998 consisted of
$1,069,000 of cash, $1,620,000 of short-term investments and $500,000 available
under a line of credit with Union Bank of California.

The decrease in total cash and investments during the three months ended June
30, 1998 was attributable to the purchase of capital assets, primarily in India
in connection with the occupation of a new building in Calcutta, combined with
decreases in accounts payable, accrued expenses, deferred maintenance revenue
and other current liabilities, and increases in prepaid and other current
assets, offset by a decrease in accounts receivable.

The Company has a $500,000 line of credit with Union Bank of California. The
line of credit bears interest at the prime rate. This credit line is
collateralized by substantially all of the assets of the Company.  The line of
credit expires on December 1, 1998.  As of June 30, 1998, there was no principal
or accrued interest outstanding under the line of credit.

During fiscal 1998 and the first quarter of fiscal 1999, the Company experienced
a decrease in Southeast Asia revenues as a result of a downturn in economic
conditions in key Asian markets.  Payment from the Company's customers in these
markets has been hampered by difficulty in obtaining favorable foreign exchange
resulting in approximately $892,000 in past-due receivables from Asian customers
at June 30, 

                                       8
<PAGE>
 
1998. The Company expects to collect the past-due receivables from Asian
customers throughout fiscal 1999 net of the allowance for doubtful accounts.

The Company believes that its current cash and short-term investment balances
and cash generated from operations and borrowings available under the Company's
line of credit will provide adequate working capital to fund the Company's
operations at currently anticipated levels through June 30, 1999. To the extent
that such amounts are insufficient to finance the Company's working capital
requirements, the Company will be required to raise additional funds through
public or private equity or debt financings.  There can be no assurance that
such additional financings will be available, if needed, or, if available, will
be on terms satisfactory to the Company.

IMPACT OF YEAR 2000

Many existing software programs use only two digits to identify the year in the
date field. If such programs are not corrected, date data concerning the Year
2000 could cause many computer applications to fail, lock-up or generate
erroneous results.

The Company is in the process of identifying and assessing its mission-critical
systems related to the Year 2000 and will commit the resources necessary to
resolve any potential Year 2000 issues. Although the Company is addressing such
issues in what it considers to be sufficient time prior to the century rollover,
there can be no assurance that there will be no interruption of operations or
other limitations of system functionality, or that the Company will not incur
substantial costs to avoid such occurrences. The Company has determined that it
will not need to modify or replace significant portions of its software sold to
customers, as it does not contain any date-specific material.

The Company is currently assessing the cost to remediate its Year 2000 issues.
Although the actual cost to remediate these issues is not yet fully known, based
upon information to date, it is expected that the remediation will not have a
material impact on the Company's financial condition or operating results.

In addition, the Company has initiated communications with its significant
suppliers and large customers to determine the extent to which the Company's
internal applications and other interface systems are vulnerable to those third
parties' failure to remedy their own Year 2000 issues.  There is no guarantee
that other companies' systems on which the Company's systems rely will be timely
converted and would not have an adverse effect on the Company's systems.


IMPACT OF RECENTLY ISSUED ACCOUNTING STANDARDS


As of April 1, 1998, the Company adopted SFAS No. 130, Reporting Comprehensive
Income. SFAS No. 130 establishes new rules for the reporting and display of
comprehensive income and its components; however, the adoption of this statement
had no impact on the Company's reported net income or stockholders' equity.
SFAS No. 130 requires unrealized gains or losses on the Company's available-for-
sale investments and foreign currency translation adjustments, which prior to
adoption were reported separately in stockholders' equity, to be included in
other comprehensive income. The prior year Consolidated Statement of
Stockholders' Equity will be reclassified at year-end fiscal 1999 to conform to
the requirements of SFAS No. 130. During the first quarter of fiscal 1999 and
1998, total comprehensive (loss)/income was ($282,000) and $3,000, respectively.

In December 1997, the FASB issued SFAS No. 131, Disclosures about Segments of an
Enterprise and Related Information, which requires the Company to disclose
certain information about reportable operating segments in complete sets of
financial statements of the Company and in condensed financial statements of
interim periods.  The Company adopted SFAS No. 131 in the first quarter of
fiscal 1999 with no material impact on the financial statements.

                                       9
<PAGE>
 
PART II -- OTHER INFORMATION

ITEM 1.  LEGAL PROCEEDINGS

         None

ITEM 2.  CHANGES IN SECURITIES
 
         None

ITEM 3.  DEFAULTS UPON SENIOR SECURITIES

         None

ITEM 4.  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

         None

ITEM 5.  OTHER INFORMATION

         None

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

         (a)  Exhibits

                27.1    Financial Data Schedule

         (b)  Reports on Form 8-K

                None

                                       10
<PAGE>
 
                                   SIGNATURES
                                   ----------
                                        
In accordance with the requirements of the Exchange Act, the registrant has duly
caused this report to be signed on its behalf by the undersigned, thereunto duly
authorized.


Date:  August 14, 1998

                                    RESEARCH ENGINEERS, INC.


                                    By: /s/ WAYNE BLAIR
                                        ---------------
                                        Wayne Blair
                                        Chief Financial Officer, Secretary
                                        and Treasurer (principal financial
                                        and accounting officer)

                                       11
<PAGE>
 
                                 EXHIBIT INDEX
                                 -------------
                                      
Exhibit 27.1   Financial Data Schedule  

                                       12