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                                                                    Exhibit 99.1




                                                Contact:   Thomas E. Daman
                                                           Dennis M. Thies
                                                           Southdown, Inc.
                                                           (713) 650-6200
                                                           
                                                           George E. Uding, Jr.
                                                           R. Breck Denny
                                                           Medusa Corporation
                                                           (216) 371-4000
FOR IMMEDIATE RELEASE
- ---------------------

           SOUTHDOWN, INC. AND  MEDUSA CORPORATION AGREE TO MERGE
           ------------------------------------------------------ 
                          IN $1 BILLION TRANSACTION
                          -------------------------

     - Combination Creates Second-Largest Cement Producer in the U.S. -

                - Transaction is Expected to be Accretive  -


         HOUSTON, TEXAS AND CLEVELAND HEIGHTS, OHIO -- March 18, 1998 --
Southdown, Inc.,  (NYSE:SDW) and Medusa Corporation (NYSE:MSA), leading U.S.
producers of cement, today announced that they have signed a definitive
agreement under which Southdown and Medusa will merge in a stock-for-stock
transaction that will make Southdown the second-largest producer of cement in
the United States with 10.8 million tons of capacity.  The combined company
will be well-positioned to capitalize on strong industry dynamics and will
have strong prospects for future growth.

         Under the terms of the agreement, which has been approved by the
boards of directors of both companies, Medusa shareholders will receive .88
shares of Southdown for each Medusa




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share.  Based on the closing prices of  Southdown and  Medusa common stock on
Tuesday, March 17, 1998, the transaction results in an implied value for Medusa
common stock of $61.22 per share and a 17% premium for Medusa shares.  On that
basis, the total value of the proposed transaction is $1 billion.  The
transaction will be tax-free to shareholders and is intended to be accounted
for by Southdown as a pooling of interests.  Excluding one-time costs directly
related to the transaction,  Southdown expects the merger to be accretive to
1998 earnings with anticipated overhead and distribution cost savings.

         Clarence C. Comer, President and Chief Executive Officer of Southdown
said, "The merger with Medusa further establishes Southdown as the largest
domestically owned cement manufacturer in the U.S.  This transaction should
give Southdown a greater opportunity to capitalize on current strong industry
fundamentals and the expected growth in cement consumption as a result of the
proposed increases in Federal and state infrastructure spending.  The expanded
network of preheater/precalciner facilities created by this combination will be
the most modern and efficient plant system in the U.S. and should have the
ability to cost-effectively expand capacity and increase earnings."

         "The combination will create a significantly larger company with
greater financial flexibility, a stronger balance sheet, higher market
capitalization and greater earnings and cash flows," Mr. Comer continued, "all
of which should enhance our ability to realize our growth potential and pursue
attractive business opportunities in the future.  Medusa's operations
complement our existing asset base and the combined network of plants and
distribution





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terminals provides broad coverage of the market east of the Mississippi, as
well as significant distribution flexibility to reduce shipping costs.  The
broader geographic scope should lessen the company's exposure to regional
cyclical downturns.  Moreover, we believe that there are potentially
significant cost savings to be realized by reducing corporate overhead."

         Robert S. Evans, Medusa's Chairman and Chief Executive Officer, said,
"This transaction provides increased value to Medusa shareholders.  In
addition, Medusa shareholders will have an ongoing equity interest in a larger
and stronger company with improved long-term growth potential and investment
liquidity.  The combined company should also benefit from Medusa's expertise in
its construction aggregates and specialty limestone businesses, which provides
an enhanced platform for future growth.  We look forward to working with
Clarence Comer and his management team to successfully integrate our two
companies for the benefit of our shareholders, customers and employees."

         The combined company will have a market capitalization of
approximately $2.7 billion (based on Southdown's 3/17/98 closing stock price);
combined 1997 revenues of approximately $1.1 billion and net income of
approximately $154 million, excluding one time charges directly related  to the
transaction.   Following the completion of the transaction, Southdown will
continue to be headquartered in Houston, Texas, and Mr. Comer will continue to
serve as President and Chief Executive Officer.  Mr. Evans will join
Southdown's Board of Directors along with Medusa's President and Chief
Operating Officer, George E. Uding, Jr.  Certain of





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Medusa's executive officers and directors, including Mr. Evans and Mr. Uding,
have given Southdown their irrevocable proxies to vote in favor of the
transaction.

         Completion of the transaction is subject to required approvals by
shareholders of both companies, the expiration of applicable waiting periods
under the antitrust laws, registration of the shares of Southdown's stock
issuable in the transaction under the securities laws, and other customary
closing conditions.  Southdown and Medusa have both cancelled their existing
stock repurchase programs as previously approved by their respective boards of
directors.  This transaction is expected to close by the end of June 1998.

         Southdown was advised by Lehman Brothers with respect to this
transaction which included rendering a fairness opinion.  Medusa was advised by
J.P. Morgan, which also  provided a fairness opinion.

         Medusa Corporation produces and sells portland and masonry cements;
mines, processes, and sells aggregates, home and garden and industrial
limestone products; and provides construction services for highway safety.
Medusa's operations are principally in the eastern half of the United States.

         Southdown, Inc. is one of the leading U.S. cement and ready-mixed
concrete companies.  The Company manufactures cement in eight plants located in
Southern California, Colorado, Florida,





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Kentucky, Ohio, Pennsylvania, Tennessee and Texas.  The Company markets
ready-mixed concrete products in its two largest markets, Florida and Southern
California.


This document includes forward looking statements within the meaning of Section
27A of the Securities Act of 1933, as amended, and Section 21E of the
Securities Exchange Act of 1934, as amended.  These statements are based on
current expectations, estimates and projections about the general economy and
Southdown's and Medusa's lines of business and are generally identifiable by
statements containing words such as "expects," "believes," "estimates" or
similar expressions.  Statements related to future performance involve certain
assumptions, risks and uncertainties, many of which are beyond the control of
Southdown or Medusa, and cannot be guaranteed.  Although Southdown and Medusa
believe that their respective expectations reflected in such forward looking
statements are based upon reasonable assumptions, they can give no assurance
that those expectations will be achieved.  Important factors that could cause
actual results to differ materially from those expectations include, among
others, foreign and domestic price competition, cost effectiveness, changes in
environmental regulation, and general economic and market conditions such as
interest rates, the availability of capital and the cyclical nature of the
construction industry.  The reader is cautioned to consider such disclosures in
conjunction with the forward looking statements included herein ("Cautionary
Disclosures").  Subsequent written and oral forward looking statements
attributable to Southdown or Medusa or persons acting on their behalf are
expressly qualified in their entirety by reference to these Cautionary
Disclosures.


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