<PAGE>   1
                                                                     EXHIBIT 3.2

                                                          FEDERAL IDENTIFICATION

                                                          NO. 04-2814792


                        THE COMMONWEALTH OF MASSACHUSETTS

                             WILLIAM FRANCIS GALVIN
                          Secretary of the Commonwealth
              One Ashburton Place, Boston, Massachusetts 02108-1512

                              ARTICLES OF AMENDMENT
                    (GENERAL LAWS, CHAPTER 156B, SECTION 72)



We,  Eric R. Giler                                                   , President
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and  David W. Duehren                                                    , Clerk
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of   Brooktrout Technology, Inc.                                               ,
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                           (Exact name of corporation)


located at    410 First Avenue, Needham, MA 02194                              ,
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                (Street address of corporation in Massachusetts)


certify that these Articles of Amendment affecting articles numbered:


                                       III
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          (Number those articles 1, 2, 3, 4, 5 and/or 6 being amended)


of the Articles of Organization were duly adopted at a meeting held on
    May 29           , 1996     , by vote of:
---------------------    -------



 4,362,363 shares of       Common           of 6,016,803 shares outstanding;
-----------          --------------------     -----------
                         (type, class & series, if any)



___________shares of _______________________of___________shares outstanding; and
                         (type, class & series, if any)



___________shares of _______________________of___________shares outstanding;
                         (type, class & series, if any)





(1)**being at least a majority of each type, class or series outstanding and
entitled to vote thereon:

(1) For amendments adopted pursuant to Chapter 156B, Section 70.
(2) For Amendments adopted pursuant to Chapter 156B Section 71.


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To change the number of shares and the par value (if any) of any type, class or
series of stock which the corporation is authorized to issue, fill in the
following:

The total presently authorized is:

___________________________________________________________________________
                                            |
          WITHOUT PAR VALUE STOCKS          |     WITH PAR VALUE STOCKS
--------------------------------------------|------------------------------
    TYPE    | NUMBER OF SHARES |    TYPE    | NUMBER OF SHARES | PAR VALUE 
------------|------------------|-------------------------------|-----------
 Common:    |      XXXX        | Common:    |    7,500,000     |   $ .01
------------|------------------|------------|------------------|-----------
            |                  |            |                  |
------------|------------------|------------|------------------|-----------
 Preferred: |      XXXX        | Preferred: |      100,000     |   $1.00
------------|------------------|-------------------------------|-----------
            |                  |            |                  |
____________|__________________|____________|__________________|___________


Change the total authorized to:

___________________________________________________________________________
                                            |
          WITHOUT PAR VALUE STOCKS          |     WITH PAR VALUE STOCKS
--------------------------------------------|------------------------------
    TYPE    | NUMBER OF SHARES |    TYPE    | NUMBER OF SHARES | PAR VALUE 
------------|------------------|-------------------------------|-----------
 Common:    |      XXXX        | Common:    |   25,000,000     |   $ .01
------------|------------------|------------|------------------|-----------
            |                  |            |                  |
------------|------------------|------------|------------------|-----------
 Preferred: |      XXXX        | Preferred: |      100,000     |   $1.00
------------|------------------|-------------------------------|-----------
            |                  |            |                  |
____________|__________________|____________|__________________|___________


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The foregoing amendment(s) will become effective when these Articles of
Amendment are filed in accordance with General Laws, Chapter 156B, Section 6
unless these articles specify, in accordance with the vote adopting the
amendment, a later effective date not more than thirty days after such filing,
in which event the amendment will become effective on such later date.

Later effective date:_______________________________.

SIGNED UNDER THE PENALTIES OF PERJURY, this   29   day of     MAY     , 19 96 ,
                                           --------      -------------    -----


        /s/ Eric R. Giler                                            , President
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            Eric R. Giler

        /s/ David W. Duehren                                             , Clerk
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            David W. Duehren


*Delete the inapplicable words


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                        THE COMMONWEALTH OF MASSACHUSETTS


                              ARTICLES OF AMENDMENT
                    (GENERAL LAWS, CHAPTER 156B, SECTION 72)
                    ========================================



I hereby approve the within Articles of Amendment and, the filing fee in the
amount of $ ______ having been paid, said articles are deemed to have been filed
with me this __________ day of________________________ 19_________.




    Effective date:________________________________________________________






                             WILLIAM FRANCIS GALVIN
                          Secretary of the Commonwealth















                         TO BE FILLED IN BY CORPORATION
                      PHOTOCOPY OF DOCUMENTS TO BE SENT TO:

                              Laurie I. Gelb, Esq.
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                          Goodwin, Procter & Hoar, LLP
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                        Exchange Place, Boston, MA 02109
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                                 (617) 570-1035
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