Dick Simon Declines Moyes Offer;
            Board will Permit Shareholders to Consider Tender

SALT LAKE CITY,  May 23  /PRNewswire/  -- Simon  Transportation  Services,  Inc.
(Nasdaq:  SIMN)  today  announced  that  Richard D.  Simon,  Chairman  and Chief
Executive  Officer,  has turned  down an offer made by Jerry  Moyes to  purchase
shares of Simon Class A and Class B Common  Stock at a price of $7.00 per share.
Mr. Simon also  declined Mr.  Moyes'  request that Mr. Simon convert his Class B
Common Stock into Class A Common Stock.

Although  Mr.  Simon  will not sell,  the  Company  announced  that its Board of
Directors  will not  stand in the way of Mr.  Moyes'  tender  offer of $7.00 per
share to the  shareholders of the Company for a period expiring August 31, 2000.
The  Board  has  adopted  resolutions  waiving  the  application  of  applicable
anti-takeover  statues to Mr. Moyes' offer during such period.  According to the
Company,  its executive  officers and directors,  including members of the Simon
family, have indicated that they will not accept Mr. Moyes' offer.

"We  continue to believe that our stock is  undervalued,  trading on May 22nd at
only 62% of book value or $5.63 per  share,"  said Mr.  Simon.  Simon also noted
that the Company has lowered its operating  ratio over the last four quarters by
a total of 6.5 points.  "By August 2000, the Company will retire its debt on its
last two terminal  facilities and will own all Company  properties free of debt.
Our  financial  position  has improved  significantly,  and we feel no financial
pressure to enter into a transaction at this time," added Simon.

Simon also  reported  that its Board of Directors  invited Mr. Moyes to join the
Board of Directors, but the offer was declined.

Founded in 1955,  Simon  Transportation  Services is a North American  truckload
carrier  specializing  in  temperature-controlled   delivery  of  food  products
throughout the continental United States, Canada and Mexico.

This  press  release  contains   certain   forward-looking   statements.   These
forward-looking  statements are subject to certain risks and uncertainties  that
could cause actual results to differ  materially from those  projected.  Without
limitation,  these  risks  and  uncertainties  include  economic  recessions  or
downturns in customers' business cycles,  excessive increases in capacity within
the truckload markets,  decreased demand for transportation  services offered by
the Company,  availability and compensation of qualified drivers,  the potential
that  customers  may not  agree  to rate  increases,  and the  possibility  that
customers may renege on current fuel surcharge agreements. Readers should review
and consider the various  disclosures  made by the Company in this press release
and in its reports to its  stockholders  and periodic  reports on Forms 10-K and
10-Q.

Note:  Additional  information about Simon Transportation Services, Inc., may be
accessed at www.simn.com on the Internet.

CONTACT: Shirley  Thompson,  President, Rita  Tuttle, V.P., Director of Investor
Relations, or  Bevo Beaven,  Senior  Account  Executive,  all  of  Carl Thompson
Associates,  Inc.,  800-959-9677;  or  Alban B. Lang, Chief Financial Officer of
Simon Transportation Services, 801-924-7000.