Exhibit (a)(1)(I)



                   JERRY MOYES ANNOUNCES CONSENT SOLICITATION
                      AND WAIVES CONDITION TO TENDER OFFER
                         FOR ALL OUTSTANDING SHARES OF
                       SIMON TRANSPORTATION SERVICES INC.
                               AT $7.00 PER SHARE

                 FOR IMMEDIATE RELEASE: THURSDAY, JUNE 8, 2000

     Phoenix, Az.--Jerry Moyes announced today that he has commenced his consent
solicitation to assume control of the board of directors of Simon Transportation
Services Inc.  Mr. Moyes also waived one of the conditions contained in his
pending tender offer to purchase up to all of the outstanding Class A and Class
B common shares of Simon Transportation Services Inc. for $7.00 net cash per
share.

     Mr. Moyes stated: "Today I filed definitive consent solicitation materials
with the SEC and began distributing the consents to Simon Transportation's
stockholders.  The consent solicitation is an important step in support of my
tender offer.  I need the consents to gain due diligence access, to ensure that
any impediments to my gaining control of the board are removed, and to ensure
that waivers of all anti-takeover statutes are effective at a level that will
permit me to complete the tender offer."

     Mr. Moyes continued: "I also have waived the condition to my offer that
450,000 Class B common shares deemed to be beneficially owned by Richard D.
Simon be tendered in the offer.  I will not require that Mr. Simon sell his
shares or convert his Class B shares to Class A shares as a condition of my
offer. The company's SEC filings indicate that Mr. Simon, the company's Chairman
and CEO, and Kelle Simon, the company's newly appointed President, both recently
sold all of the more than 45,000 aggregate shares of Simon Transportation
formerly held in their 401(k) retirement accounts.  I hope those sales indicate
a willingness to sell additional shares in the offer.

     I would welcome Mr. Simon's voluntary participation in the offer in order
to reduce the disproportionate voting effect of his Class B shares, which carry
two votes per share.  With those Class B shares, Mr. Simon controls 24.9% of the
total voting power with only 14.1% of the total shares.  Mr. Simon's double-
voting shares will require a large number of the independent stockholders to
participate in the tender offer for me to purchase the majority voting control
the Simon Board has required for their waiver of the applicable anti-takeover
statutes to be effective.

     In a recent letter to stockholders, the Simon Board accused me of
attempting to gain control of the company without paying for it. With the
double-voting stock, the classified board of directors, and five family members
on the board, it is the Simons who are attempting to control the company without
a corresponding economic investment. I


have made my $7.00 offer to all stockholders and am firmly committed to pursuing
it. I call on Dick Simon to participate significantly in the offer or convert
his Class B shares to Class A shares and create a level playing field for all
stockholders."

Other Important Information:
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     This press release is for information purposes only and is not an offer to
buy or the solicitation of an offer to sell any of the shares of Simon
Transportation and is not a solicitation of a proxy or written consents.  The
offer to buy Simon Transportation shares is being made only pursuant to the
Offer to Purchase and related materials that Mr. Moyes has sent to Simon
Transportation stockholders and has filed as an exhibit to the tender offer
statement.  The tender offer statement and the consent solicitation materials
contain important information that stockholders should consider before making
any decision regarding their shares.  You can obtain the tender offer statement,
as well as other filings containing information about Mr. Moyes and Simon
Transportation, without charge, at the Securities and Exchange Commission's
Internet site (www.sec.gov).  Copies of the tender offer statement and other SEC
filings also will be available, without charge, from the Information Agent for
the offer, as identified below:

      The Information Agent for the Offer and the Consent Solicitation is:

                            MacKenzie Partners, Inc.
                                156 Fifth Avenue
                               New York, NY 10010
                         (212) 929-5500 (call collect)
                         Call Toll-Free (800) 322-2885
                           Fax Number (212) 929-0308