<PAGE>   1
                                                                     EXHIBIT 4.1

                          [Specimen Stock Certificate]

                            ODYSSEY HEALTHCARE, INC.

              INCORPORATED UNDER THE LAWS OF THE STATE OF DELAWARE

<Table>
<S>                                                <C>
                  COMMON STOCK                     SEE REVERSE FOR CERTAIN DEFINITIONS
         THIS CERTIFICATE IS TRANSFERABLE                       AND LEGENDS
IN NEW YORK, NEW YORK AND GLENDALE, CALIFORNIA.              CUSIP 67611V 10 1
</Table>

             THIS CERTIFIES THAT

               IS THE OWNER OF


         FULLY PAID AND NON-ASSESSABLE SHARES OF THE PAR VALUE OF $.001 PER
SHARE OF THE COMMON STOCK OF

                            ODYSSEY HEALTHCARE, INC.

transferable on the books of the Corporation in person or by duly authorized
attorney upon surrender of this certificate properly endorsed. This certificate
and the shares represented hereby are issued and shall be held subject to the
provisions of the laws of the State of Delaware and to all of the provisions of
the Certificate of Incorporation and the Bylaws of the Corporation, as amended
from time to time (copies of which are on file at the office of the
Corporation), to all of which the holder of this certificate by acceptance
hereof assents. This certificate is not valid until countersigned by the
Transfer Agent and registered by the Registrar.

         IN WITNESS WHEREOF, the said Corporation has caused this certificate to
be signed by its duly authorized officers and its corporate seal to be hereunto
affixed.

         Dated:

                                [corporate seal]

         [Facsimile Signature]                    [Facsimile Signature]

              PRESIDENT                                SECRETARY

COUNTERSIGNED AND REGISTERED:
                  U.S. STOCK TRANSFER CORPORATION
                                    TRANSFER AGENT AND REGISTRAR

BY

                                            AUTHORIZED SIGNATURE


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                            ODYSSEY HEALTHCARE, INC.

THE CORPORATION WILL FURNISH WITHOUT CHARGE TO EACH STOCKHOLDER WHO SO REQUESTS
A STATEMENT OF THE POWERS, DESIGNATIONS, PREFERENCES AND RELATIVE,
PARTICIPATING, OPTIONAL OR OTHER SPECIAL RIGHTS OF EACH CLASS OF STOCK OR SERIES
THEREOF OF THE CORPORATION, AND THE QUALIFICATIONS, LIMITATIONS OR RESTRICTIONS
OF SUCH PREFERENCES AND/OR RIGHTS. SUCH REQUEST MAY BE MADE TO THE CORPORATION
OR THE TRANSFER AGENT.

     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>                                   <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                            Under Uniform Gifts to Minors
                of survivorship and not as                             Act _________________________
                tenants in common                                                   (State)
</Table>

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

     For Value Received, ___________________ hereby sell(s), assign(s) and
transfer(s) 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 capital stock represented by the within certificate, and do(es) hereby
irrevocably constitute and appoint _____________________________ Attorney to
transfer the said stock on the books of the within-named Corporation with full
power of substitution in the premises.

Dated
      -----------------
                                        SIGNATURE OR REGISTERED OWNER(S):

                  NOTICE:

        THE SIGNATURE(S) TO THIS       X
        ASSIGNMENT MUST CORRESPOND      ----------------------------------------
        WITH THE NAME(S) OF THE                      (SIGNATURE)
        REGISTERED OWNER(S) AS
        WRITTEN UPON THE FACE OF THE   X
        CERTIFICATE IN EVERY            ----------------------------------------
        PARTICULAR WITHOUT ALTERATION                (SIGNATURE)
        OR ENLARGEMENT OR ANY CHANGE
        WHATSOEVER.

                                        ----------------------------------------
                                        THE SIGNATURE(S) SHOULD 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 RULE 17Ad-15 UNDER THE SECURITIES
                                        EXCHANGE ACT OF 1934, AS AMENDED.
                                        ----------------------------------------
                                        SIGNATURES(S) GUARANTEED BY:




                                        ----------------------------------------