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                                                                     EXHIBIT 4.1

                       FORM OF SUBSCRIPTION CERTIFICATE

THE TERMS AND CONDITIONS OF THE RIGHTS OFFERING ARE SET FORTH IN THE COMPANY'S
PROSPECTUS DATED ____________ (THE "PROSPECTUS") AND ARE INCORPORATED HEREIN BY
     REFERENCE.  COPIES OF THE PROSPECTUS ARE AVAILABLE UPON REQUEST FROM
          COMPUTERSHARE INVESTOR SERVICES AS THE SUBSCRIPTION AGENT.


STOCKHOLDER NAME AND ADDRESS:   ___________________________________
                                ___________________________________
                                ___________________________________
CERTIFICATE NO.:__________

                        CERTIFICATE FOR ________RIGHTS

                             TIPPERARY CORPORATION
               INCORPORATED UNDER THE LAWS OF THE STATE OF TEXAS

                           SUBSCRIPTION CERTIFICATE

 EVIDENCING ____ NON-TRANSFERABLE SUBSCRIPTION RIGHTS TO PURCHASE A COMPARABLE
         NUMBER OF SHARES OF THE COMMON STOCK OF TIPPERARY CORPORATION

                     SUBSCRIPTION PRICE: $_____ PER SHARE

               VOID IF NOT EXERCISED BEFORE THE EXPIRATION DATE
                        (AS DEFINED IN THE PROSPECTUS)

REGISTERED OWNER:

     THIS CERTIFIES THAT the registered owner whose name is inscribed herein is
the owner of the number of Subscription Rights set forth above, each of which
entitles the owner to subscribe for and purchase one share of the Common Stock,
par value $.02 per share (the "Common Stock"), of Tipperary Corporation, a Texas
corporation (the "Company"), on the terms and subject to the conditions set
forth in the Company's Prospectus dated _____________, 2001 and instructions
relating thereto on the reverse side hereof.  The non-transferable Subscription
Rights represented by this Subscription Certificate may be exercised by duly
completing Section 1 on the reverse side hereof.  Special issuance or delivery
instructions may be specified by completing Section 2 on the reverse side
hereof.

     THE SUBSCRIPTION RIGHTS EVIDENCED BY THIS SUBSCRIPTION CERTIFICATE ARE NOT
TRASNFERABLE, SUCH SUBSCRIPTION RIGHTS MAY NOT BE EXERCISED UNLESS THE REVERSE
SIDE HEREOF IS COMPELTED AND SIGNED.

Dated: ________________

______________________________          ______________________________
David L. Bradshaw                       Elaine R. Treece
Chief Executive Officer                 Secretary
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                     SECTION 1 - EXERCISE AND SUBSCRIPTION

The undersigned irrevocably exercises Subscription Rights to subscribe for
shares of the Company's Common Stock, as indicated below, on the terms and
subject to the conditions specified in the Company's Prospectus dated
________________, relating to the offering of such Subscription Rights, receipt
of which is hereby acknowledged.

     (a)  Number of shares of the Company's Common Stock subscribed for pursuant
          to the Basic Subscription Privilege:____________________

     (b)  Number of shares of the Company's Common Stock subscribed for pursuant
          to the Over-Subscription Privilege:_____________________

YOU MAY NOT EXERCISE THE OVER-SUBSCRIPTION PRIVILEGE UNLESS YOUR BASIC
SUBSCRIPTION PRIVILEGE HAS BEEN EXERCISED IN FULL.

     (c)  Total Subscription Price (total number of shares subscribed for
          pursuant to both the Basic Subscription Privilege plus the Over-
          Subscription Privilege multiplied by the Subscription Price of
          $_______ per share):  $_________________.

METHOD OF PAYMENT (CHECK ONE)

[_]  Uncertified personal check, payable to Computershare Investor Services as
     Subscription Agent for Tipperary Corporation.  Please note that funds paid
     by uncertified personal check may take at least five business days to
     clear.  Accordingly, subscription rights holders who wish to pay the
     purchase price by means of an uncertified personal check are urged to make
     payment sufficiently in advance of the expiration date to ensure that such
     payment is received and clears by the expiration date, and are urged to
     consider payment by means of a certified or bank check, money order or wire
     transfer of immediately available funds.

[_]  Certified check or bank check drawn on a U.S. bank or money order, payable
     to Computershare Investor Services as Subscription Agent for  Tipperary
     Corporation.

[_]  Wire transfer directed to the account maintained by Computershare Investor
     Services at

                                Union Bank & Trust
                                100 Broadway
                                Denver, Colorado 80209
                                (303) 744-3221
                                ABA # 102000908
                                Credit Account #85-02961
                                Account Name:  Computershare Trust Company, Inc.
                                               Escrow Agent

If the amount enclosed or transmitted is not sufficient to pay the purchase
price for all shares of Common Stock that are stated to be subscribed for, or if
the number of shares of Common Stock being subscribed for is not specified, the
number of shares of Common Stock subscribed for will be assumed to be the
maximum number that could be subscribed for upon payment of such amount.  If the
amount enclosed or transmitted exceeds the purchase price for all shares of
Common Stock that the undersigned has the right to subscribe for under the Basic
Subscription Privilege plus the Over-Subscription Privilege (such excess amount,
the "Subscription Excess"), the Subscription Agent shall return the Subscription
Excess to the subscriber without interest or deduction.
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           SECTION 2 - SPECIAL ISSUANCE OR DELIVERY INSTRUCTIONS FOR
                         SUBSCRIPTION RIGHTS HOLDERS:

To be completed ONLY if the certificate representing the Common Stock is to be
issued in a name other than that of the registered holder or is to be sent to an
address other than that shown above.  (See the Instructions included with this
Rights Certificate.)  Do not forget to complete the guarantee of signature(s)
section below.

Please issue the certificate representing the Common Stock in the following name
and/or deliver to the following address:

Name:___________________________        Soc. Sec. #/Tax ID#:____________________
Address:________________________________________________________________________
        ________________________________________________________________________

                  ACKNOWLEDGMENT--THE SUBSCRIPTION ORDER FORM
                      IS NOT VALID UNLESS YOU SIGN BELOW

I/We acknowledge receipt of the Prospectus and understand that after delivery of
this Subscription Certificate to the Company's Subscription Agent, I/we may not
modify or revoke this Subscription Certificate.  Under penalties of perjury,
I/we certify that the information contained herein, including the social
security number or taxpayer identification number given above, is correct.  If
the Special Issuance or Delivery Instructions for Subscription Rights Holders
are completed, I/we certify that although the certificate representing the
Common Stock is to be issued in a name other than the registered holder,
beneficial ownership of the Common Stock will not change.

The signatures below must correspond with the name of the registered holder
exactly as it appears on the books of the Company's transfer agent without any
alteration or change whatsoever.

Subscriber's Signature(s):________________________    Date:_____________________
                          ________________________    Date:_____________________

If signature is by trustee(s), executor(s), administrator(s), guardian(s),
attorney(s)-in-fact, agent(s), officer(s) of a corporation or another acting in
a fiduciary or representative capacity, please provide the following information
(please print).  (See the Instructions included with this Rights Certificate.)

Name:_________________________________    Capacity:___________________________
Address:______________________________    Phone:______________________________
______________________________________    Soc. Sec. # or Tax ID#:_____________

                           GUARANTEE OF SIGNATURE(S)

All Subscription Rights Holders who specify special issuance or delivery
instructions must have their signatures guaranteed by an Eligible Institution,
as defined in Rule 17Ad-15 of the Securities Exchange Act of 1934, as amended.
(See the Instructions.)

Signature Guaranteed by:___________________________________
                                Eligible Institution
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                                   EXHIBIT B

                        Payment of Funds to the Company

                                _____________________
                                ABA Routing #____________
                                Credit Account #_______________
                                Account Name:   Tipperary Corporation
                                                Concentration Account
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                                   EXHIBIT C

                           Compensation for Services

                  (proposal dated __________ to be attached)