<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 10-Q

                   QUARTERLY REPORT UNDER SECTION 13 OR 15 (d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

 For Quarter Ended March 31, 1998               Commission File Number 0-4539

                             TRANS-INDUSTRIES, INC.
                             ----------------------

             (Exact name of registrant as specified in its charter)

          Delaware                                   13-2598139
          --------                                   ----------
 (State or other jurisdiction of        (I.R.S. Employer Identification No.)
 incorporation or organization)

                  2637 S. Adams Road, Rochester Hills, MI 48309
                  --------------------------------------------- 
                     (Address)                    (Zip Code)

        Registrant's Telephone Number, including Area Code (248) 852-1990

     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 and Exchange Act
of 1934 during the preceding 12 months and (2) has been subject to such filing
requirements for the past 90 days. YES  X NO
                                   ---      ---

The number of shares outstanding of registrant's Common stock, par value $.10
per share, at March 31, 1998 was 3,074,400.


<PAGE>   2
                 TRANS-INDUSTRIES, INC. AND SUBSIDIARY COMPANIES

                FORM 10-Q - FOR THE QUARTER ENDED MARCH 31, 1998

                                    INDEX

PART I.   Financial Information

Item 1.           FINANCIAL STATEMENTS

                  A.       Consolidated Statements of Earnings ---
                              Three months ended March 31, 1998 and 1997.

                  B.       Consolidated Balance Sheets ---
                              March 31, 1998 and December 31, 1997.

                  C.       Consolidated Statements of Cash Flows ---
                              Three months ended March 31, 1998 and 1997.

                  D.       Notes to Consolidated Financial Statements.


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


PART II.  Other Information

Item 1.           LEGAL PROCEEDINGS

Item 5.           OTHER INFORMATION

Item 6.           EXHIBITS AND REPORTS ON FORM 8-K

                  SIGNATURES


                                       2

<PAGE>   3



A.                   TRANS-INDUSTRIES, INC. AND SUBSIDIARIES
                     
                  CONSOLIDATED STATEMENTS OF EARNINGS (Unaudited)


<TABLE>
<CAPTION>


                                                                         For 3 Months Ended:
                                                                         ------------------
                                                                      3/31/98            3/31/97
                                                                      -------            -------
<S>                                                                   <C>                 <C>
1.   Gross sales less discounts, returns and allowances               $9,202,796         $7,989,776

2.   Cost of goods sold                                                5,989,735          5,038,495
                                                                       ---------         ----------
3.   Gross Profit                                                      3,213,061          2,951,281

4.   Selling, general and administrative exp.                          2,083,175          1,986,580
                                                                       ---------         ----------

5.   Operating income/(loss)                                           1,129,886            964,701

6.   Other (income)/ expense
         Interest expense                                                141,219            175,723
         Other income                                                    (22,390)          (169,090)
                                                                       ---------         ----------
         Total other (income)/expense                                    118,829              6,633
                                                                       ---------         ----------

7.   Earnings/(loss) before income taxes                               1,011,057            958,068

8.   Income tax expense/(benefit)                                        278,000            337,000
                                                                       ---------         ----------

9.   Net profit/(loss)                                                 $ 733,057           $621,068
                                                                       =========         ==========
10.  Earnings per share:
         Basic                                                         $     .24         $      .20
                                                                       =========         ==========
         Diluted                                                       $     .23          $     .20
                                                                       =========         ==========

11.  Dividends per share                                                 __                  __
                                                                       =========         ==========

</TABLE>
See Notes to Financial Statements


                                       3
<PAGE>   4

                     TRANS-INDUSTRIES, INC. AND SUBSIDIARIES
B.
                           CONSOLIDATED BALANCE SHEETS
<TABLE>
<CAPTION>

     ASSETS                                                                       
Current Assets                              3/31/98           12/31/97            
                                          (Unaudited)         (Audited)           
                                          ----------          --------
<S>                                        <C>              <C>
     Cash                                  $  168,668       $   132,297           
     Accounts receivable                    8,218,941         8,433,468           
     Inventories (Note 2)                   7,175,208         6,824,438           
     Prepaid expenses                         676,295           247,123           
     Deferred income taxes                    444,000           444,000           
                                          -----------        ----------                                        
                                                                                  
     Total current assets                  16,683,112        16,081,326           
                                                                                  
Property, Plant & Equipment, at Cost                                              


     Land                                     314,503           314,503                             
     Land Improvements                        126,660           126,660           
     Buildings                              4,992,828         4,992,360           
     Machinery & equipment                  8,091,618         7,848,472           
                                          -----------        ----------                                        
                                           13,525,609        13,281,995           
     Less: accumulated                                                            
           depreciation                    (8,474,960)       (8,269,084)           
                                          -----------        ----------                                        
     Net plant and equipment                5,050,649         5,012,911           
                                          -----------        ----------                                        
Other Assets                                                                      

                                                                                  
     Investments in affiliates                 10,000            10,000           
                                                                                  
     Patents, licenses & trademarks,                                              
     net of accumulated amortization          234,345           231,937           
                                                                                  
     Excess of cost of investment in                                              
     stock of subsidiary over equity in                                           
     underlying net assets of acquisition     167,140           178,283           
                                                                                  
     Sundry                                   104,471           104,471               
                                          -----------        ----------                                        
                                                                                  
Total assets                              $22,249,717       $21,618,928             
                                          ===========       ===========
</TABLE>
See Notes to Financial Statements.

<TABLE>
<CAPTION>


        LIABILITIES AND STOCKHOLDERS EQUITY


       Current Liabilities                           3/31/98          12/31/97
                                                 (Unaudited)         (Audited)
                                                 ----------         -----------
<S>                                            <C>                 <C>
        Notes Payable (Note 5)                  $  3,028,764        $ 3,503,262
        Current installments
            - Long term debt (Note 5)                191,136            193,389
        Accounts payable - trade                   3,052,421          2,419,154
        Accrued liabilities                        1,324,589          1,703,684
        Income taxes                                 256,000             88,000
                                                ------------          ---------
        Total current liabilities                  7,852,910          7,907,489

        Deferred income taxes - Non-current          197,000            197,000

      Long term debt

        Current portion shown above (Note 5)       3,499,469          3,561,838
        Other non-current liabilities                315,652            312,355

      Stockholders'  Equity

      Preferred stock of $1.00 par value
        per share - authorized 500,000
        shared; none issued                               --                 --

        Common stock of $.10 par value per
        share - authorized 10,000,000 shares;
        3,074,400 shares issued and 3,074,400
        outstanding at 3/31/98                       307,440            307,320


        Additional paid-in  capital                4,070,246          4,062,116
        Retained earnings                          6,006,304          5,273,244
      Foreign currency translation                       696             (2,434)
                                                ------------       ------------
                                                  10,384,686          9,640,246
                                                ------------       ------------ 
    Total liabilities and stockholders' equity  $ 22,249,717       $ 21,618,928
                                                ============       ============
                                                  
</TABLE>
See Notes to Financial Statements.














                                       4


<PAGE>   5
                             TRANS-INDUSTRIES, INC.
                      Consolidated Statements of Cash Flows
C.              For the Three Months Ended March 31, 1998 and 1997


<TABLE>
<CAPTION>

                                                                           Three Months Ended March 31
                                                                        --------------------------------
                                                                            1998                  1997
                                                                            ----                  ----          
                                                                       ( Unaudited)          ( Unaudited)
                                                                       -----------           -----------
<S>                                                              <C>                  <C>
CASH FLOWS FROM OPERATING ACTIVITIES
Net income (loss)                                                $        733,060        $     621,068
Adjustments to reconcile net income (loss)
to net cash provided by operations:
     Depreciation/Amortization                                            215,407              199,573
     Decrease (increase) in accts. receiv.                                214,527        (     670,632)
     Decrease (increase) in inventory                            (        350,770)       (     316,735)
     Decrease (increase) in prepaid exp.                         (        429,172)       (      43,237)
     Increase (decrease) in accts. payable                                633,267        (     265,330)
     Increase (decrease) in accr. liab.                          (        379,095)       (      70,327)
     Increase (decrease) in income taxes                                  168,000              137,000
     (Gain) loss on sale of fixed assets                                       -0-       (     148,689)
                                                                 ----------------        -------------
Net Cash Provided (Used) by Operations                                    805,224        (     557,309)

CASH FLOWS FROM INVESTING ACTIVITIES
     Purchase of fixed assets                                    (        244,410)       (     164,304)
     Proceeds from sale of property and equipment                              -0-             205,000
                                                                 ----------------        -------------

Net Cash Provided (Used) by Investing                            (        244,410)              40,696

CASH FLOWS FROM FINANCING ACTIVITIES
     Net increase (repayment) of long-term
     borrowings                                                  (         61,325)       (     146,323)
     Net proceeds (payment) of credit line                       (        474,498)             511,817
     Common stock issued through ESOP                                       8,250                   -0-
                                                                 ----------------        -------------   
Net Cash Provided (Used) by Financing                            (        527,573)             365,494

Foreign currency translation                                                3,130        (      37,911)
                                                                 ----------------        -------------

Net Increase in Cash                                                       36,371        (     189,030)
Cash at beginning of year                                                 132,297              358,764
                                                                 ----------------        -------------
Cash at end of quarter                                           $        168,668        $     169,734
                                                                 ================        =============
Supplemental Disclosures:
     Interest paid                                               $        140,087        $     165,312
     Income taxes (refunded) paid, net                           $        110,000        $     200,000


</TABLE>

See Notes to Financial Statements

                                      5
<PAGE>   6
D.                  TRANS-INDUSTRIES, INC. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS



1.   Basis of Presentation

     The financial  information  presented as of any date other than December 31
     has been  prepared  from the  Company's  books and records without audit.
     Financial information  as of December 31 has been derived from the audited
     financial statements  of the Company.  In the opinion of  management,  all
     adjustments  consisting of normal  recurring adjustments, necessary for a
     fair presentation of the financial information for the periods indicated,
     have  been included.  For  further information regarding the Company's
     accounting policies,  refer to the consolidated financial statements and
     related notes included in the Company's  annual report on form 10-K for the
     year ended December 31, 1997.


2.   Inventories

     The major components of inventories are:

<TABLE>
<CAPTION>
                                                    3/31/98              12/31/97
                                                    -------              --------
<S>               <C>                               <C>                  <C>
                  Raw Materials                     $3,385,694          $3,471,708
                  Work in Process                    1,216,319           1,178,684
                  Finished Goods                     2,573,195           2,174,046
                                                    ----------          ----------
                                                    $7,175,208          $6,824,438
                                                    ==========          ==========
</TABLE>



3.   Principles of Consolidation

     There have been no significant changes in the principles of  consolidation 
     since our most recent audited financial statements.


4.   Significant Accounting Policies

     There have been no significant changes in the accounting policies since our
     most recent audited financial statements.

     On January 1, 1998, the Corporation adopted Financial  Accounting Standards
     Board (the "FASB") issued  Statement No. 130,  "Reporting of  Comprehensive
     Income" ("SFAS130"),  which establishes standards for reporting and display
     of comprehensive income and its


                                       6
 
<PAGE>   7

    D.               TRANS-INDUSTRIES, INC. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS



     components  (revenues,  expenses,  gains  and  losses)  in a  full  set of
     financial statements.  This statement also requires that all items that are
     required to be recognized under accounting  standards as  components of
     comprehensive income be reported in a financial statement that is displayed
     with  the  same prominence  as other financial  statements.  Consolidated
     statements  of comprehensive  income for each of the three month periods
     ended March 31, 1998 and 1997 have been omitted,  as comprehensive income
     for each of the periods does not materially differ from reported earnings.

<TABLE>
<S>                                                                                             <C>
5.   Long-Term Debt

     Long-term debt at March 31, 1998 consisted of the following:

     Trans-Industries, Inc., $3,840,000 term note, payable in                                   $3,421,378
     monthly installments of $39,333 which includes interest 
     at 1/4% over the  bank's prime lending rate, and a
     balloon payment of $3,137,124 in October 1999.  The
     note is secured by substantially all the assets of
     Trans-Industries, Inc. and subsidiaries.

     Transmatic Europe Ltd., mortgage note, payable in monthly                                     155,675
     installments of $3,476 plus interest at 9.99%.   The 
     mortgage is secured by certain property and is due
     August 9, 2003.

     Term note, payable in monthly installments of $896                                            113,552
     including interest at a rate of 6%.  The note is due January 21, 2002.

                                                                                                 ---------
                                                                                                 3,690,605
     Less current installments                                                                   ( 191,136)
                                                                                                 ---------
     Long-term debt                                                                             $3,499,469
                                                                                                ==========



</TABLE>

                                       7

<PAGE>   8
                     TRANS-INDUSTRIES, INC. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

5.    Long-Term Debt (continued)

     The Trans-Industries,  Inc.  term loan agreement  contains  restrictive
     provisions relating  principally to the maintenance of working capital, net
     worth, ratio of debt to net worth, payment of dividends, and acquisition of
     fixed  assets.  At March 31, 1998 the Company  was in  compliance  with all
     provisions.

     The  Company  also  has a  secured  $6,500,000  line  of  credit  of  which
     $3,028,764  was  utilized  at March 31,  1998.  Interest  is charged at the
     bank's prime lending rate. This line of credit expires on July 1, 1999. The
     line is secured  by  substantially  all of the assets of  Trans-Industries,
     Inc. and its domestic subsidiaries.


6.   Earnings Per Share

     The following is a reconciliation of the numerator and denominator of the 
     basic and diluted earnings per share computations.

<TABLE>
<CAPTION>


                                                      EARNINGS               SHARES          PER SHARE
                                                     (NUMERATOR)          (DENOMINATOR)       AMOUNT
                                                     ----------           -------------     ---------
<S>                                           <C>                         <C>                <C>
     Qtr. ended March 31, 1998
         Basic earnings per share:
              Earnings available to common
                  stockholders                          $733,057             3,072,900         .24
              Effect of dilutive securities
                  Stock options                          --                     58,427        (.01)
         Diluted earnings per share:                    --------             ---------      ------
              Earnings available to stockholders
              plus assumed conversions                  $733,057             3,131,327         .23
                                                        ========             =========      ======
                                                  
</TABLE>

<TABLE>
<CAPTION>

                                                      EARNINGS               SHARES          PER SHARE
                                                     (NUMERATOR)          (DENOMINATOR)       AMOUNT
                                                     ----------           -------------     ---------
<S>                                                   <C>                  <C>                <C>
     Qtr. ended March 31, 1997
         Basic earnings per share:
              Earnings available to common
                  stockholders                          $621,068             3,073,250         .20
              Effect of dilutive securities
                  Convertible debt                         3,535               107,124         .00
         Diluted earnings per share:                    --------             ---------      ------
              Earnings available to stockholders
              plus assumed conversions                  $624,603             3,180,374         .20
                                                        ========             =========      ======

</TABLE>

 
                                      8
<PAGE>   9


                     TRANS-INDUSTRIES, INC. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


7.   Stock Changes

     In February of 1998,  the  Company  received a request from an employee to
     exercise his stock option for 1200 shares of common stock at a price of
     $6.875 per share.  Accordingly,  the Company issued a certificate for 1200
     shares.




                                      9


<PAGE>   10
                     TRANS-INDUSTRIES, INC. AND SUBSIDIARIES

Item 2.           MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                     CONDITION AND RESULTS OF OPERATIONS
                    For Three Months Ended March 31, 1998


Sales and Earnings

     Sales for the  quarter ended March 31,  1998 were  $9,202,796  compared to
$7,989,776 for the same period a year ago.  This increase of  $1,213,020  is
primarily attributable to an increase in sales of the Company's  lighting
products utilized on mass transit vehicles.

     During the first quarter of 1998,  the  Company  realized a net profit of
$733,057 on sales of  $9,202,796.  For the same  period of the prior  year,  the
Company reported net profit of $621,068 on sales of $7,989,776. This increase in
net profit of $111,989 can, in part, be attributed to the increased sales volume
achieved.  The  Company  was also able to utilize a portion of the  foreign  tax
credits  generated  from prior year losses.  This foreign  credit  permitted the
Company to reduce its overall  income tax rate to 27.5  percent for the quarter.
Net profit per share for the first  quarter was $.24 and $.20 for 1998 and 1997,
respectively. Net profit per share was computed on the adjusted weighted average
number of shares  outstanding  during the quarter for 1998 and 1997,  which were
3,072,900 and 3,073,250, respectively.

Inventories

     Inventory valuation is based upon the lower of cost or market. At March 31,
1998,  consolidated  inventories  were $7,175,208  compared to $6,479,327 a year
ago. This increase of $695,881 is to accommodate the growth in sales volume.

Interest

     Interest expense  amounted to  approximately  $141,000 and $176,000 for the
first quarter of 1998 and 1997,  respectively.  This decrease of $35,000 was the
result of  average  debt  levels  being less  during  the first  quarter of 1998
compared to 1997.

Financial Condition

     Current financial resources coupled with anticipated funds from operations
are expected to meet funding requirements  for the remainder of the year, based
upon present needs.

     As noted in Item 1, "Legal Proceedings", the Company was paid $3,023,773.00
on May 1, 1998. This amount represents  damages awarded by the Court in a patent
infringement  case.  After paying related fees, the Company expects to net
approximately $2.4 million before paying related income taxes.


                                       10
<PAGE>   11

                           PART II - OTHER INFORMATION



Item 1.                         LEGAL PROCEEDING

     The  Company is the  plaintiff  in a patent  infringement  lawsuit.  During
November  of 1993,  an  advisory  jury  recommended  a decision  in favor of the
Company.  In April of 1994,  the  judge  concurred  with the  advisory  jury and
ordered that the  defendant be enjoined  from any further  manufacture,  use, or
sale of the accused patented device.  It was also ordered that the defendant pay
approximately  $3 million in damages.  During 1994,  the defendant  appealed the
case based on the lower courts  interpretation  of the law. On May 2, 1995,  the
Company was notified that the U.S. Circuit Court of Appeals changed the District
Courts  ruling that the  defendant  literally  infringed  the patent  instead of
infringement by equivalents. Further the Court of Appeals remanded the case back
to the Federal District Court for further  determination of damages. On April 9,
1998,  the  District  Court  awarded  the Company  $3,023,773.00  in damages and
$1,119,588.00  in  interest.  On May 1, 1998,  the  defendant  paid the  damages
awarded to the Company and indicated they intended to appeal the interest award.
At the time of this  writing,  the  defendant  has not filed an appeal  with the
court. A final outcome is expected in 9 - 12 months.


Item 5.                        OTHER INFORMATION

     On  August  6,  1997 the  Company  repurchased  all  remaining  convertible
subordinated debentures outstanding. This purchase eliminates the possibility of
any dilution of common stock which would have  resulted  from the  conversion of
these debentures.


Item 6.              EXHIBITS AND REPORTS ON FORM 8-K

     (b) Form 8K dated May 4, 1998;  receipt of damage award and  Declaration of
Special Dividend.


                                       11
<PAGE>   12
                                   SIGNATURES



     Pursuant to the  requirements of the Securities Exchange Act of l934, the
registrant has duly  caused  this report to be signed on its  behalf by the
undersigned thereunto duly authorized.


                                                TRANS-INDUSTRIES, INC.
                                                



Date:   May 12, 1998                             /s/     Kai Kosanke
        ------------                             --------------------------
                                                 Kai Kosanke, Treasurer
                                                 and Chief Financial Officer



Date:   May 12, 1998                             /s/     Paul Clemo
        ------------                             -------------------
                                                 Paul Clemo
                                                 Assistant Treasurer






                                       12
<PAGE>   13


                                EXHIBIT INDEX


Exhibit No.                     Description

   27                           Financial Data Schedule