<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 December 31, 1997



[_]  TRANSITION REPORT UNDER SECTION 13 OR 15(d) OF THE SECURITES 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 5,677,710 on February 1, 1998.
<PAGE>
 
PART I -- FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS

                   RESEARCH ENGINEERS, INC. AND SUBSIDIARIES
                          CONSOLIDATED BALANCE SHEET
                               DECEMBER 31, 1997
                                  (Unaudited)
              (In thousands, except share and per share amounts)
<TABLE> 
<S>                                                                     <C>
                                    ASSETS
Current assets:                                                          
  Cash and cash equivalents                                             $   827
  Short term investments                                                  1,541
  Accounts receivable (net of allowance for doubtful accounts of $89)     2,776
  Deferred income taxes                                                     396
  Notes and related party loans receivable                                   90
  Prepaid expenses and other current assets                                 497
                                                                        -------
        Total current assets                                              6,127
                                                                        
Property, plant and equipment, net                                        2,945
Goodwill (net of accumulated amortization of $413)                        1,175
Other assets                                                                865
                                                                        -------
                                                                        $11,112
                                                                        =======
                     LIABILITIES AND STOCKHOLDERS' EQUITY          
                                                                   
Current liabilities:                                               
  Accounts payable                                                      $   233
  Accrued expenses                                                          493
  Income taxes payable                                                      312
  Deferred maintenance revenue                                              884
  Current portion of long-term bank debt                                    190
  Other                                                                      48
                                                                        -------
        Total current liabilities                                         2,160
                                                                   
Long-term bank debt                                                       1,831
Deferred income taxes                                                        55
                                                                        -------
        Total liabilities                                                 4,046
                                                                        -------
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 5,677,710 shares                                   57
  Additional paid-in capital                                              6,594
  Retained earnings                                                         554
  Unrealized loss on investments                                            (42)
  Foreign currency translation adjustment                                   (97)
                                                                        -------
        Total stockholders' equity                                        7,066
                                                                        -------
                                                                        $11,112
                                                                        =======
</TABLE> 

See accompanying notes to consolidated financial statements.

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

<TABLE> 
<CAPTION> 
                                       Three Months  Three Months  Nine Months   Nine Months 
                                          Ended         Ended         Ended         Ended     
                                       December 31,  December 31,  December 31,  December 31,  
                                           1997          1996          1997          1996
                                       ------------  ------------  ------------  ------------  
<S>                                    <C>           <C>           <C>           <C>     
Net revenues:                                                                    
  Product sales                         $   2,787     $   2,350     $   7,802     $   6,191
  Maintenance and support                     493           380         1,367         1,059
                                        ---------     ---------     ---------     ---------
    Total net revenues                      3,280         2,730         9,169         7,250
                                                                                 
Cost of revenues                              131           222           480           561
                                        ---------     ---------     ---------     ---------
    Gross profit                            3,149         2,508         8,689         6,689
                                        ---------     ---------     ---------     ---------
Operating expenses:                                                              
  Selling, general and administrative   $   2,163     $   1,882     $   6,668     $   4,732
  Research and development                    543           418         1,497         1,207
  Acquired in-process research and                                               
   development costs                          450           715           450           715
                                        ---------     ---------     ---------     ---------
    Total operating expenses                3,156         3,015         8,615         6,654
                                        ---------     ---------     ---------     ---------
    Operating income/(loss)                    (7)         (507)           74            35
                                        ---------     ---------     ---------     ---------
Other (income)/expense:                                                          
  Interest, net                               (14)          (56)          (36)          (30)
  Other                                       (17)          (22)          (63)          (91)
                                        ---------     ---------     ---------     ---------
Income/(loss) before income taxes              24          (429)          173           156
                                                                                 
Income tax expense                            150            79           170           236
                                        ---------     ---------     ---------     ---------
    Net income/(loss)                   $    (126)    $    (508)    $       3     $     (80)
                                        =========     =========     =========     =========
Net income/(loss) per common share:                                              
  Basic                                 $   (0.02)    $   (0.09)    $    0.00     $   (0.02)
  Diluted                               $   (0.02)    $   (0.09)    $    0.00     $   (0.02)
                                                                                 
Average number of common shares                                                  
 used in computing net income/(loss)                                             
 per common share:                                                               
  Basic                                 5,699,618     5,701,000     5,701,373     5,014,889
  Diluted                               5,699,618     5,701,000     5,778,497     5,014,889
</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> 
                                                    Nine Months   Nine Months
                                                       Ended         Ended
                                                    December 31,  December 31, 
                                                        1997          1996  
                                                    ------------  ------------
<S>                                                 <C>           <C>  
Cash flows from operating activities:
  Net income/(loss)                                   $     3       $    (80) 
  Adjustments to reconcile net income to net cash      
   provided (used) by operating activities:            
    In-process research and development                   450            715 
    Depreciation and amortization                         359            347
    Deferred income taxes                                 (80)            (1) 
    Changes in operating assets and liabilities:       
      Accounts receivable                                (638)          (416)  
      Notes and related party loans receivable            (27)           (76)  
      Prepaid expenses and other current assets           (29)          (321)
      Other assets                                       (609)          (216) 
      Accounts payable, accrued expenses and           
       other current liabilities                         (168)          (350)  
      Deferred maintenance revenue                         97            133  
      Income taxes payable                                 43            143
      Other long-term liabilities                         (21)           (59)  
                                                      -------       --------
          Net cash used in operating activities          (620)          (181) 
                                                      -------       --------
Cash flows from investing activities:                  
  Purchase of property, plant and equipment              (396)          (183) 
  Purchase of short-term investments                   (3,459)        (3,206)
  Sale of short-term investments                        3,571          1,685
  Payments to acquire companies, net of cash           
   acquired                                              (550)        (1,513)
  Proceeds from repayment of related party note        
   receivable                                               -             48
                                                      -------       --------
          Net cash used in investing activities          (834)        (3,169)
                                                      -------       --------
Cash flows from financing activities:                  
  Net proceeds from issuance of common stock                9          6,469
  Payments to repurchase common stock                    (200)             - 
  Repayment of bank debt                                 (107)        (1,907) 
  Repayment of stockholder loans                            -           (481)
                                                      -------       --------
          Net cash (used in) provided by               
           financing activities                          (298)         4,081 
                                                      -------       --------
          (Decrease) increase in cash and              
           cash equivalents                            (1,752)           731
                                                       
Cash and cash equivalents, beginning of period          2,579            528 
                                                      -------       --------
Cash and cash equivalents, end of period              $   827       $  1,259
                                                      =======       ========
</TABLE> 

See accompanying notes to consolidated financial statements.

                                       4
<PAGE>
 
                   RESEARCH ENGINEERS, INC. AND SUBSIDIARIES
                  NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                               DECEMBER 31, 1997
                                  (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 and nine months ended December 31, 1997 and 1996, the
     financial position at December 31, 1997, and the cash flows for the nine
     months ended December 31, 1997 and 1996, 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 and nine months ended December 31, 1997 are not
     necessarily indicative of the results to be expected for the full year
     ended March 31, 1998.


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.   NET EARNINGS PER SHARE

     In the quarter ended December 31, 1997, the Company adopted Statement of
     Financial Accounting Standards No. 128, "Earnings Per Share ("EPS")." This
     statement replaces the previously reported primary and fully diluted EPS.
     Unlike primary EPS, basic EPS excludes any dilutive effects of options. All
     net income/(loss) per share amounts have been restated to conform to the
     SFAS No. 128 requirements.

                                       5
<PAGE>
 
     The following table illustrates the computation of basic and diluted net
income/(loss) per share (in thousands):

<TABLE> 
<CAPTION> 

                             Three Months Three Months Nine Months  Nine Months
                                Ended        Ended        Ended        Ended
                             December 31, December 31, December 31, December 31,
                                 1997         1996         1997         1996
                             ------------ ------------ ------------ ------------
<S>                          <C>          <C>          <C>          <C> 
Numerator:
Numerator for basic and 
  diluted net income/(loss)
  per share - net 
  income/(loss)                 $ (126)      $ (508)      $    3      $  (80)
                                ------       ------       ------      ------
                                                                     
Denominator:                                                         
Denominator for basic net                                            
  income/(loss) per share -                                          
  average number of common                                           
  shares outstanding during                                          
  the period                     5,700        5,701        5,701       5,015
                                                                     
Incremental common shares                                            
  attributable to exercise                                           
  of outstanding options             -            -           77           -
                                ------       ------       ------      ------
Denominator for diluted net                                          
  income/(loss) per share        5,700        5,701        5,778       5,015
                                ------       ------       ------      ------
                                                                     
Basic net income/(loss)                                              
  per share                     $(0.02)      $(0.09)      $ 0.00      $(0.02)
                                ------       ------       ------      ------
Diluted net income/(loss)                                            
  per share                     $(0.02)      $(0.09)      $ 0.00      $(0.02)
                                ------       ------       ------      ------
</TABLE> 


     The computation of diluted loss per share for the three-month periods ended
     December 31, 1997 and 1996 and the nine-month period ended December 31,
     1996 excluded the effect of incremental common shares attributable to the
     exercise of outstanding common stock options because their effect was
     antidilutive.


5.   ACQUISITION

     On October 13, 1997, the Company purchased certain assets of AXA
     Corporation ("AXA"), a software developer. The purchase price of $550,000
     in cash was allocated as follows (in thousands):

<TABLE>
     <S>                                               <C>
     Acquired in-process research and development      $450
     Property and equipment                               3
     Goodwill                                            97
                                                       ----
                                                       $550
                                                       ====
</TABLE>

     The goodwill associated with the AXA acquisition will be amortized over
     five years on a straight-line basis.


6.   STOCK REPURCHASE

     On December 16, 1997, in accordance with Amendment No. 1 to the Agreement
     and Plan of Reorganization dated March 8, 1996 between the Company and ADL
     Pipe, Inc., the Company repurchased 26,290 shares of common stock for
     $200,000.

                                       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 and
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 and nine months ended December 31, 1997, as compared to
the Company's results of operations for the three and nine months ended December
31, 1996.


RESULTS OF OPERATIONS FOR THE THREE MONTHS ENDED DECEMBER 31, 1997 AND 1996 AND
NINE MONTHS ENDED DECEMBER 31, 1997 AND 1996

Net revenues - Net revenues for the quarter ended December 31, 1997 increased by
$550,000 (20%) to $3,280,000, as compared to $2,730,000 for the quarter ended
December 31, 1996. For the nine months ended December 31, 1997, revenues
increased by $1,919,000 (27%) to $9,169,000 from $7,250,000 for the nine months
ended December 31, 1996. These increases in net revenues were primarily
attributable to the Company's continued growth in overseas markets.

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. Product maintenance revenues are amortized over the length of the
maintenance contract, which is usually twelve months.

International net revenues as a percentage of total revenues for the quarter
ended December 31, 1997 increased to 58%, up from 51% for the quarter ended
December 31, 1996. For the nine months ended December 31, 1997, international
revenues increased to 61%, up from 56% for the nine months ended December 31,
1996. The increase in international revenues for the periods was primarily the
result of increased revenues from the Asian market as the Company's products
continue to gain market acceptance and the result of the acquisition of QSE
(Bristol) Limited in December 1996. 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 either the three month or the six
month periods ended December 31, 1997 and 1996.

Gross profit - Gross profit increased by $641,000 (26%) to $3,149,000 in the
quarter ended December 31, 1997 as compared to $2,508,000 for the quarter ended
December 31, 1996. Gross profit increased by $2,000,000 (30%) to $8,689,000 for
the nine months ended December 31, 1997 as compared to $6,689,000 for the nine
months ended December 31, 1996. These increases were primarily due to increased
sales volume.

Selling, general and administrative expense - Selling, general and
administrative expense increased by $281,000 (15%) to $2,163,000 for the quarter
ended December 31, 1997 as compared to $1,882,000 for the quarter ended December
31, 1996, and decreased as a percentage of net revenues to 66% from 69% in the
comparable quarter of the prior year. Selling, general and administrative
expense increased by $1,936,000 (41%) to $6,668,000 in the nine months ended
December 31, 1997 as compared to $4,732,000 for the nine 

                                       7
<PAGE>
 
months ended December 31, 1996, and increased as a percentage of net revenues to
73% from 65% in the comparable period of the prior year. Selling expenses in
both the three and nine month periods increased primarily as a result of higher
commissions being paid associated with higher net revenues in the overseas
markets. General and administrative expenses in both the three and nine month
periods increased due to the addition of administrative, customer service and
technical support personnel, combined with increases in professional fees, and
in the nine-month period, due to a one time charge for severance paid to a
former QSE (Bristol) Limited employee during the first quarter of fiscal 1998.

Research and development expense - Research and development expense increased by
$125,000 (30%) to $543,000 in the quarter ended December 31, 1997 as compared to
$418,000 for the quarter ended December 31, 1996, and increased as a percentage
of net revenues to 17% from 15% in the comparable quarter of the prior year.
Research and development expense increased by $290,000 (24%) to $1,497,000 in
the nine months ended December 31, 1997 as compared to $1,207,000 for the nine
months ended December 31, 1996, and decreased as a percentage of net revenues to
16% from 17% in the comparable nine months of the prior year. The increases in
research and development expense are primarily due to costs associated with the
finalization of STAAD/Pro, the Company's next generation structural engineering
product.

Acquired in-process research and development expense - The acquired in-process
research and development expense of $450,000 and $715,000 for the three months
and nine months ended December 31, 1997 and 1996, respectively, relates to the
acquisition of the animation software assets of AXA, Inc. during October 1997
and the acquisition of QSE (Bristol) Limited during December 1996. Included in
the assets acquired were costs of $450,000 and $715,000 related to AXA and QSE,
respectively, of research and development in process. In the opinion of
management, the technological feasibility of the acquired development had not
yet been established and the technology had no future alternative uses at the
time of the acquisition, and accordingly, these amounts were expensed in their
respective periods.

Other (income) expense - Net interest (income) expense decreased by $47,000 to
($31,000) in the quarter ended December 31, 1997 as compared to ($78,000) for
the quarter ended December 31, 1996. Net interest (income) expense decreased by
$22,000 to ($99,000) in the nine months ended December 31, 1997 as compared to
($121,000) for the nine months ended December 31, 1996. The Company completed
its initial public offering during the second quarter of fiscal 1997, the
proceeds of which were used to pay off debt and increase investments. In
addition, the Company entered into certain loan agreements at the end of fiscal
1997. Therefore, the Company had an increase in interest expense during the
three months and nine months ended December 31, 1997 as compared to the same
periods in the prior year.

Income taxes - Income tax expense increased by $71,000 to $150,000 in the
quarter ended December 31, 1997 as compared to $79,000 for the quarter ended
December 31, 1996. This increase in income tax expense is due to the increase in
sales in the foreign subsidiaries. Income tax expense decreased by $66,000 to
$170,000 in the nine months ended December 31, 1997 as compared to $236,000 for
the nine months ended December 31, 1996. This decrease in income tax expense is
primarily due to a pretax loss in the United States for the nine months ended
December 31, 1997 and the related tax benefit for the net operating loss that
was recorded. The effective tax rates are greater than 100% due to the
international earnings.

LIQUIDITY AND CAPITAL RESOURCES

Certain statements contained in this report, including those contained in
"Results of Operations for the Three Months Ended December 31, 1997 and 1996 and
the Nine Months Ended December 31, 1997 and 1996" 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, including those
acquired from AXA and QSE (Bristol) Limited, 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 

                                       8
<PAGE>
 
Form 10-KSB/A for the fiscal year ended March 31, 1997 which was filed with the
Securities and Exchange Commission on August 19, 1997 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 December 31, 1997 consisted of
$827,000 of cash, $1,541,000 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 nine months ended December
31, 1997 was primarily attributable to purchases of capital assets and other
assets consisting mainly of purchased technology, the purchase of AXA, an
increase in accounts receivable, and the repurchase of common stock combined
with a decrease in accounts payable and accrued expenses offset by an increase
in deferred maintenance.

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 December 31, 1997 there was no
principal or accrued interest outstanding under the line of credit.

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 December 31, 1998. 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.

Based on an assessment of the Year 2000 issue, the Company has determined that
it will not need to modify or replace significant portions of its software, and
therefore, no resources will need to be allocated to this issue.

                                       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

                 10.34  AXA, Inc. Asset Purchase Agreement

                 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:  February 13, 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 10.34    AXA, Inc. Asset Purchase Agreement

Exhibit 27.1     Financial Data Schedule

                                       12