<PAGE>   1
                                                                   EXHIBIT 4.1

                            FORMED UNDER THE LAWS OF
                               THE STATE OF TEXAS

<TABLE>
<S>                                     <C>                                                      <C>
                                                                                                       PAR VALUE $.01 PER SHARE
                                        
     NUMBER                             CERTIFICATE FOR COMMON SHARES OF BENEFICIAL INTEREST                    SHARES
  CS                                                    AMRESCO CAPITAL TRUST
                                                A TEXAS REAL ESTATE INVESTMENT TRUST

THIS CERTIFICATE IS TRANSFERABLE                                                                          CUSIP 031919 10 3
     IN NEW YORK, NY                         SEE REVERSE FOR CERTAIN RESTRICTIONS                SEE REVERSE FOR CERTAIN DEFINITIONS

                                                                                                                     

THIS CERTIFIES THAT





IS THE REGISTERED HOLDER OF
 

                                FULLY PAID AND NONASSESSABLE COMMON SHARES OF BENEFICIAL INTEREST OF

Amresco Capital Trust (the "Trust"). A full statement of all the designations, preferences, limitations and relative rights of the
shares of each class or series which the Trust is authorized to issue, to the extent they have been fixed and determined, and the
authority of the Trust Managers to fix and determine the designations, preferences, limitations and relative rights of authorized
series, as set forth in the Declaration of Trust, as may be amended from time to time, is on file with the County Clerk of Dallas
County, Texas, a copy of which will be furnished to the record holder of the certificate without charge upon written request to
the Trust at its principal place of business. This certificate and the shares represented hereby are negotiable and transferable on
the books of the Trust by the registered holder hereof in person or by attorney upon surrender of this certificate properly
endorsed or signed. This certificate is not valid until countersigned and registered by a Transfer Agent and Registrar.

     Witness the facsimile signature of the Trust's duly authorized officers.

Dated                                                                                       COUNTERSIGNED AND REGISTERED:
                                                                                                 THE BANK OF NEW YORK
                                                    [AMRESCO CAPITAL TRUST SEAL]                     TRANSFER AGENT AND REGISTRAR
                                                                                   
/s/ MARK D. GIBSON      /s/ MICHAEL L. MCCOY                                                BY  [ILLEGIBLE]
    PRESIDENT                  SECRETARY                                                                     AUTHORIZED SIGNATURE

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AMERICAN BANK NOTE COMPANY             APR 15, 1998 fm
3504 ATLANTIC AVENUE
SUITE 12                               056272fc
LONG BEACH, CA 90807                   
(582) 989-2335
(FAX) (582) 426-7450          7B       Proof _____ NEW
<PAGE>   2
                             AMRESCO CAPITAL TRUST

        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>
        <S>                                             <C>
        TEN COM -- as tenants in common                 UNIF GIFT MIN ACT -- __________ Custodian ___________
        TEN ENT -- as tenants by the entireties                                (Cust)               (Minor)
        JT TEN  -- as joint tenants with right of                            Under Uniform Gifts to Minors
                   survivorship and not as tenants                           Act ____________________________
                   in common                                                               (State)

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


For Value Received, __________________ 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 

__________________________________________________________________________________

__________________________________________________________________________________

_________________________________________________________________ Common Shares
of Beneficial Interest represented by the within Certificate, and do hereby 
irrevocably constitute and appoint _______________________________________________
______________________________________________________________________ Attorney
to transfer the said stock on the books of the within-named Trust with full
power of substitution in the premises.

Dated  ______________________________


              NOTICE
       THE SIGNATURE(S) TO
       THIS ASSIGNMENT MUST         X_____________________________________________
       CORRESPOND WITH THE                           (SIGNATURE)
       NAME(S) AS WRITTEN    
       UPON THE FACE OF THE ----->   
       CERTIFICATE IN EVERY
       PARTICULAR WITHOUT           X ____________________________________________
       ALTERATION OR EN-                             (SIGNATURE)
       LARGEMENT OR ANY
       CHANGE WHATEVER.               THE SIGNATURE(S) MUST BE GUARANTEED BY
                                      AN ELIGIBLE GUARANTOR INSTITUTION
                                      (BANKS, STOCKBROKERS, SAVINGS AND LOAN
                                      ASSOCIATIONS AND CREDIT UNIONS WITH
                                      MEMBERSHIP IN AN APPROVED SIGNATURE
                                      GUARANTEE MEDALLION PROGRAM), PURSUANT
                                      TO SEC. RULE 17Ad-15.
                                     
                                      SIGNATURE(S) GUARANTEED BY:

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         THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO
RESTRICTIONS ON OWNERSHIP AND TRANSFER FOR THE PURPOSE OF THE TRUST'S
MAINTENANCE OF ITS STATUS AS A REAL ESTATE INVESTMENT TRUST UNDER THE INTERNAL
REVENUE CODE OF 1986, AS AMENDED (THE "CODE"). PURSUANT TO THE TRUST'S
DECLARATION OF TRUST, AND EXCEPT AS OTHERWISE PROVIDED THEREIN, NO PERSON MAY
(1) BENEFICIALLY OWN SHARES IN EXCESS OF 9.8% IN VALUE OR NUMBER OF SHARES OF
ALL OUTSTANDING SHARES OF SUCH CLASS OR (2) BENEFICIALLY OWN SHARES THAT WOULD
RESULT IN THE TRUST BEING "CLOSELY HELD" UNDER SECTION 856(h) OF THE CODE OR
OTHERWISE CAUSE THE TRUST TO FAIL TO QUALIFY AS A REIT. IF THE RESTRICTIONS ON
OWNERSHIP OR TRANSFER ARE VIOLATED, THE SHARES REPRESENTED HEREBY WILL BE
AUTOMATICALLY TRANSFERRED TO A TRUSTEE OF A CHARITABLE TRUST FOR THE BENEFIT OF
ONE OR MORE CHARITABLE BENEFICIARIES. IN ADDITION, UPON THE OCCURRENCE OF
CERTAIN EVENTS, ATTEMPTED TRANSFERS IN VIOLATION OF THE ABOVE RESTRICTIONS MAY
BE VOID. ALL TERMS IN THIS LEGEND NOT OTHERWISE DEFINED HEREIN HAVE THE
MEANINGS ASCRIBED THERETO IN THE TRUST'S DECLARATION OF TRUST, AS THE SAME MAY
BE FURTHER AMENDED FROM TIME TO TIME, A COPY OF WHICH, INCLUDING THE
RESTRICTIONS ON OWNERSHIP OR TRANSFER, WILL BE SENT WITHOUT CHARGE TO THE
RECORD HOLDER OF THE CERTIFICATE UPON WRITTEN REQUEST TO THE TRUST AT ITS
PRINCIPAL PLACE OF BUSINESS.

         AMERICAN BANK NOTE COMPANY          APR 16, 1998 fm
         3504 ATLANTIC AVENUE
         SUITE 12                            056272bk
         LONG BEACH, CA 90807
         (562) 989-2333                      proof   REV 2
         (FAX) (562) 426-7450