<PAGE>   1
                                                                     Exhibit 4.1


[NUMBER SEAL]                                                      [SHARES SEAL]
                           BANCORP RHODE ISLAND, INC.

             CHARTERED UNDER THE LAWS OF THE STATE OF RHODE ISLAND
                           PAR VALUE $0.01 PER SHARE

                                                                   CUSIP

                                             SEE REVERSE FOR CERTAIN DEFINITIONS



THIS CERTIFIES that                                              is the owner of








          FULLY PAID AND NON-ASSESSABLE SHARES OF THE COMMON STOCK OF
                           BANCORP RHODE ISLAND, INC.

transferable only on the books of the Corporation in person or by duly
authorized Attorney upon surrender of this Certificate properly endorsed.

     This Certificate is not valid unless countersigned and registered by the
Transfer Agent and Registrar.

     IN WITNESS WHEREOF, BANCORP RHODE ISLAND, INC. has caused the facsimile
signatures of its duly authorized officers and a facsimile of its corporate seal
to be hereunto affixed.

DATED:
                       [BANCORP RHODE ISLAND, INC. SEAL]

          /S/ Albert R. Rietheimer                  /S/ Merrill W. Shermann

            ALBERT R. RIETHEIMER                       MERRILL W. SHERMANN
                Treasurer                                   President


COUNTERSIGNED AND REGISTERED:
     REGISTRAR AND TRANSFER COMPANY
          (CRANFORD, NEW JERSEY)
                         TRANSFER AGENT
                          AND REGISTRAR
BY


                    AUTHORIZED SIGNATURE
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     The securities represented by this certificate are issued subject to all
the provisions of the Articles of Incorporation and By-laws of Bancorp Rhode
Island, Inc. (the "Corporation") as from time to time amended (copies of which
are on file at the main office of the Corporation), to all of which the holder
by acceptance hereof assents.

     The Corporation is authorized to issue more than one class or series of
capital stock. The Corporation will furnish to any stockholder, upon request and
without charge, a full statement of the designations, preferences, limitations,
and relative rights of the shares of each class or series authorized to be
issued.

     The following abbreviations, when used in the inscription on the face of
this certificate, shall be construed as though they were written out in full
according to applicable laws or regulations:

<TABLE>
<CAPTION>

<S>                                        <C>


TEN COM   - as tenants in common            UNIF GIFT MIN ACT................Custodian.........under
TEN ENT   - as tenants by the entireties                         (Cust)               (Minor)
JT TEN    - as joint tenants, with right        Uniform Gifts to Minors Act.........................
            of survivorship and not                                               (State)
            as tenants in common
</TABLE>


    Additional abbreviations may also be used though not in the above list.

 For Value Received,__________________ do hereby sell, assign and transfer unto

PLEASE INSERT SOCIAL SECURITY OR OTHER
  IDENTIFYING NUMBER OF ASSIGNEE
 -----------------------
/                      /
-----------------------
________________________________________________________________________________

________________________________________________________________________________
PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS INCLUDING POSTAL ZIP CODE OF ASSIGNEE

________________________________________________________________________________

________________________________________________________________________________

_________________________________________________________________________ Shares

of the Common Stock represented by the within Certificate, and do hereby
irrevocably constitute and appoint

________________________________________________________________________________

________________________________________________________________________________

Attorney to transfer the said Shares on the books of the within named
Corporation with full power of substitution in the premises.


Dated:_________________


In presence of _______________________________________

_________________________________________

NOTICE: The signature to this assignment must correspond with the name as
written upon the face of the Certificate, in every particular, without
alteration or enlargement, or any change whatever.

The signature(s) of the assignor(s) must be guaranteed hereon by a participant
in either the Securities Transfer Agent's Medallion Program (STAMP), the Stock
Exchange Medallion Program (SEMP), or the New York Stock Exchange Medallion
Program (MSP).