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[LETTERHEAD - LOGO]
                               MEDUSA CORPORATION
LEE AND MONTICELLO   -   CLEVELAND HEIGHTS, OHIO 44118   -         216/371-4000
                                                               Fax 216/371-2912

                                                                    MAIL ADDRESS
                                                                   P.O. BOX 5668
                                                                 CLEVELAND 44101



TO OUR SHAREHOLDERS:

For the fifth consecutive year, Medusa achieved record revenues and earnings.
Revenues increased 16% to $376.0 million, resulting from continued strong market
conditions for both cement and aggregates and additional sales from our three
minerals acquisitions made during the year. Net income increased 5% to $57.0
million, or $3.41 per diluted share. This compares with net income in 1996 of
$54.3 million or $3.15 per share, before an extraordinary charge of $1.8 million
or $0.10 per share related to the early retirement of debt. Our results for this
year reflect a pretax charge of approximately $4 million principally related to
certain environmental matters at our Charlevoix, Michigan plant.

Our cement operations had another excellent year, with record production and
sales. The record production is the result of our incremental capacity expansion
program which we continued this year. This program has increased our production
levels by 8% over 1993 levels, the year we began the program.

We continue to use our strong cash flow for the benefit of shareholders. Cash
flow from operations was $76.9 million, up 20% from last year. Capital spending
this year totaled $24.5 million, 24% higher than last year. We have begun a
major modernization and expansion of our Clinchfield, Georgia cement plant and
related distribution facilities. This $56 million project will significantly
reduce the cash costs of the Clinchfield complex and increase clinker capacity
by 175,000 tons annually to about 760,000 tons. We expect this project will
reach full production in the second half of 1999.

We have made significant progress in making Medusa Minerals the premier supplier
of limestone-related lawn and garden products in the eastern United States. In
January, 1997, we acquired the Sparta, New Jersey-based Lime Crest Corporation.
In late August, we acquired the stock of White Stone Company, with operations in
Castlewood, Virginia and Paradise, Pennsylvania. In October, we acquired Lee
Lime Corporation, based in western Massachusetts. In early January, 1998, we
acquired Commonwealth Stone, an aggregates producer located in Bowling Green,
Kentucky. In total, we have invested nearly $73 million in these operations.


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With these acquisitions, we have increased our capacity of high quality chemical
and white stone reserves to better serve the industrial minerals and lawn and
garden markets. In addition, these new operations have allowed us to expand our
core construction aggregates business into new markets. We have also gained
pelletized lime technology and capabilities along with significant bagging,
materials handling and warehousing expertise. We feel that with the combination
of these businesses we will provide an excellent return to shareholders.

The turnaround at James H. Drew Corporation continues. In 1997, Drew continued
to strive to be the low-cost supplier of quality construction services for
highway safety. Costs have been reduced by consolidating operations into a
single location in Indiana and divesting low-margin product lines. Drew's
strategic plan includes making the company less seasonal by increasing its
activities in warmer-climate states.

Enclosed is a press release announcing the proposed merger between Medusa and
Southdown, Inc. Your Board of Directors believes that the merger represents a
unique strategic opportunity for Medusa, creating the largest publicly-owned
cement company in the United States. The larger, financially strong combined
company should benefit from significant synergies while affording investors
enhanced investment liquidity and diversification of risk.

A special shareholders meeting to request approval of the proposed transaction
is anticipated within 60 to 90 days. You will be sent a proxy statement that
will provide detailed information on the transaction. We urge you to read it
carefully.

In closing, we thank our dedicated employees for their hard work and commitment,
and our shareholders for their continuing support.


Robert S. Evans, Chairman of the Board
George E. Uding, Jr., President

Cleveland, Ohio
March 25, 1998