1
 
                  NOTICE OF GUARANTEED DELIVERY FOR SHARES OF
                       SERIES A 8% CUMULATIVE CONVERTIBLE
                          PREFERRED STOCK OF MESA INC.
                  SUBSCRIBED FOR UNDER THE BASIC SUBSCRIPTION
                       AND THE OVERSUBSCRIPTION PRIVILEGE
 
     As set forth in the Prospectus under "The Rights Offering -- Exercise of
Rights," this form or one substantially equivalent hereto may be used as a means
of effecting subscription and payment for all shares of Mesa's Series A 8%
Cumulative Convertible Preferred Stock. Such form may be delivered by hand or
sent by telex, facsimile transmission, overnight courier or mail to the
Subscription Agent.
 
                           The Subscription Agent is:
 
                   AMERICAN STOCK TRANSFER AND TRUST COMPANY
                 Attention: Corporate Stock Transfer Department
 

                                                        
            By Mail                     By Facsimile                      By Hand
  40 Wall Street, 46th Floor           (718) 234-5001           40 Wall Street, 46th Floor
      New York, NY 10005                                            New York, NY 10005

 
                            Confirm by telephone to:
                                 (718) 921-8200
 
                             By Overnight Courier:
                      Corporate Stock Transfer Department
                           40 Wall Street, 46th Floor
                               New York, NY 10005
 
     DELIVERY OF THIS INSTRUMENT TO AN ADDRESS, OR TRANSMISSION OF INSTRUCTIONS
VIA A TELECOPY FACSIMILE NUMBER, OTHER THAN AS SET FORTH ABOVE, DOES NOT
CONSTITUTE A VALID DELIVERY
 
     The New York Stock Exchange member firm or bank or trust company which
completes this form must communicate the guarantee and the number of Shares
subscribed for (under both the Basic Subscription Privilege and the
Oversubscription Privilege) to the Subscription Agent and must deliver this
Notice of Guaranteed Delivery of Payment, guaranteeing delivery of (a) payment
in full for all subscribed shares and (b) a properly completed and signed copy
of the Subscription Certificate to the Subscription Agent prior to 5:00 p.m.,
New York City time, on the Expiration Date. Failure to do so will result in a
forfeiture of the Rights.
 
                                   GUARANTEE
 
     The undersigned, a member firm of the New York Stock Exchange or a bank or
trust company having an office or correspondent in the United States, guarantees
delivery to the Subscription Agent by the close for business on [            ,
1996], of (a) a properly completed and executed Subscription Form, and (b)
payment of the full Subscription Price for Shares subscribed for pursuant to the
Basic Subscription Privilege and any additional Shares subscribed for pursuant
to the Oversubscription Privilege, a subscription for such Shares is indicated
herein or in the Subscription Form.
 
Number of Rights to be delivered
                                ------------------------
 
Method of delivery (circle one)  A. Through DTC*
                                 B. Direct to Subscription Agent
   2
 

                                                          

- ------------------------------------------------------       ------------------------------------------------------
   Number of Shares of Basic Subscription Privilege              Number of Shares of Oversubscription Privilege

- ------------------------------------------------------       ------------------------------------------------------
                     Name of Firm                                             Authorized Signature

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                        Address                                                       Title
                                                                                                                     
- ------------------------------------------------------       Name -------------------------------------------------   
                       Zip Code                                              (Please Type or Print)

- ------------------------------------------------------       ------------------------------------------------------
                     Contact Name                                                 Phone Number

 
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* IF THE RIGHTS ARE DELIVERED THROUGH DTC, A REPRESENTATIVE OF AMERICAN STOCK
  TRANSFER AND TRUST COMPANY WILL PHONE YOU WITH A PROTECT IDENTIFICATION
  NUMBER, WHICH NEEDS TO BE RELATED BY YOU TO DTC.