<PAGE>
                                                                   EXHIBIT 10.13

         STOCK OPTION AGREEMENT dated as of the date set forth on the signature
page hereto, between QUALITY DISTRIBUTION, INC., a Florida corporation (the
"Company"), and the optionee set forth on the signature page hereto (the
"Optionee").

         The Company, whether acting through its Board of Directors (the
"Board") or a committee thereof (the "Committee") has granted to the Optionee,
effective as of the date of this Agreement, an option under the Company's 1998
Stock Option Plan (the "Plan") to purchase up to the number of shares of the
common stock, $.01 par value, of the Company (the "Shares") set forth on the
signature page hereto, on the terms and subject to the conditions set forth in
this Agreement and the Plan.

         NOW, THEREFORE, in consideration of the premises and of the mutual
agreements contained herein the parties hereto agree as follows:

1. THE PLAN.

         The terms and provisions of the Plan are hereby incorporated into this
Agreement as if set forth herein in their. entirety. In the event of a conflict
between any provision of this Agreement and the Plan, the provisions of this
Agreement shall control, further all references to the Shareholders Agreement
shall be superceded by the terms set forth herein A copy of the Plan is attached
hereto as Exhibit 2. Capitalized terms used herein and not otherwise defined
shall have the meanings ascribed thereto in the Plan.

2. OPTION; OPTION PRICE.

         On the terms and subject to the conditions of this Agreement, the
Optionee is hereby granted the option (the "Option") to purchase Shares at the
Option Price set forth on the signature page hereto. The Option shall consist of
a Tranche A Option, Tranche B Option, Tranche C Option and Tranche D Option as
set forth in the Plan. The Option is not intended to qualify for federal income
tax purposes as an "incentive stock option" within the meaning of Section 422 of
the Internal Revenue Code of 1986, as amended (the "Code").

3. TERM.

         The term of the Option (the "Option Term") shall commence on the date
hereof and expire on the tenth anniversary of the date hereof, unless the Option
shall have sooner been terminated in accordance with the terms of the Plan or
this Agreement.

4. VESTING

         The Option shall be subject to the vesting requirements of the Plan
except as set forth on Exhibit 1 attached hereto.


<PAGE>

5. EXERCISE.

         (a) Payment. The following forms of payment may be used by the Optionee
(or such other person exercising the Option in accordance with the provisions of
Section 13(c) of the Plan) upon exercise of the Option:

         (i) cash or personal or certified check payable to the Company in an
amount equal to the aggregate Option Price of the Shares with respect to which
the Option is being exercised;

         (ii) stock certificates (in negotiable form) representing Shares having
a Fair Market Value on the date of exercise equal to the aggregate Option Price
of the Shares with respect to which the Option is being exercised; or

         (iii) Vested options having an option value (the difference between the
exercised price thereof and the fair market value of the stock underlying such
option) on the date of exercise equal to the aggregate Option Price of the
Shares with respect to which the Option is exercised.

         (iv) a combination of the methods set forth in clauses (i) and (ii)
above.

         (a) Certain Terminations. Notwithstanding any provision in the Plan or
this Agreement to the contrary, in the event of a termination of employment of
the Optionee other than for "Cause" (as defined in the Employment Agreement) the
Committee shall not have the discretion to specify or limit the available forms
of payment as described in the proviso to paragraph (a) above, and the Optionee
shall be entitled to exercise the Option, to the extent it has become a Vested
Option, until 120 days following the date on which the Company shall have
notified the Optionee of the per share Fair Market Value of the Shares (which
notice shall not be given prior to the later of (i) .the date of such
termination and (ii) the date on which the Optionee ceases to be a member of the
Board), provided that the Option shall not be exercisable following the tenth
anniversary of the date of grant.

         (b) Notice. The Optionee (or such other person exercising the Option in
accordance with the provisions of Section 13(c) of the Plan) may exercise the
Option in whole or in part (but for the purchase of whole Shares only) by
delivering a written notice (the "Notice") to the Secretary of the Company. The
Notice shall state:

that the Optionee elects to exercise the Option;

         (i) the number of Shares with respect to which the Option is being
exercised (the "Optioned Shares");

         (ii) the method of payment for the Optioned Shares;


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<PAGE>

         (iii) the date upon which the Optionee desires to consummate the
purchase (which date must be prior to the termination of the Option); and

         (iv) a copy of any election filed by the Optionee pursuant to Section
83(b) of the Code.

         (c) Exercise Date. The exercise date shall be the date on which the
Company receives the Notice from the Optionee, or such later date as may be
specified in the Notice from the Optionee.

         (d) Issuance of Certificates. The Company shall issue a stock
certificate in the name of the Optionee (or such other person exercising the
Option in accordance with the provisions of Section 13(c) of the Plan) for the
Shares purchased upon exercise of an Option as soon as practicable after receipt
of the Notice and payment of the aggregate Option Price for such Shares. Neither
the Optionee nor any person exercising the Option in accordance with the
provisions of Section 13(c) of the Plan shall have any privileges as a
stockholder of the Company with respect to any Shares subject to the Option
until the date of issuance of a stock certificate.

         (e) Restrictions. No Shares shall be issued and delivered upon the
exercise of the Option unless and until the Company and/or the Optionee shall
have complied with all applicable Federal or state registration, listing and/or
qualification requirements and all other requirements of law or of any
regulatory agencies having jurisdiction. The Company shall make all reasonable
efforts to comply with such requirements that relate to the Company.

6. RESTRICTION ON TRANSFER.

         The Option may not be transferred, pledged, assigned, hypothecated or
otherwise disposed of in any way by the Optionee and may be exercised during the
lifetime of the Optionee only by the Optionee. The Option shall not be subject
to execution, attachment or similar process. Any attempted assignment, transfer,
pledge, hypothecation or other disposition of the Option contrary to the
provisions hereof, and the levy of any execution, attachment or similar process
upon the Option, shall be null and void and without effect.

7. OPTIONEE'S EMPLOYMENT.

         Nothing in the Option shall confer upon the Optionee any right to
continue to be employed by the Company or any of its Affiliates or interfere in
any way with the right of the Company or its Affiliates or stockholders, as the
case may be, to terminate the Optionee's employment or retention by the Company
or any of its Affiliates or to increase or decrease the Optionee's compensation
at any time.

8. NOTICES.

         All notices, claims, certificates, requests, demands and other
communications hereunder shall be in writing and shall be deemed to have been
duly


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<PAGE>

given and delivered if personally delivered or if sent by nationally-recognized
overnight courier guaranteeing next day delivery, by telecopy, or by registered
or certified mail, return receipt requested and postage prepaid, addressed as
follows:

(f)      if to the Company, to it at:

         Quality Distribution, Inc.
         3802 Corporex Park Drive
         Tampa, Florida 33619
         Attention: General Counsel
         Telecopier: (813) 757-2305
         Telephone:  (813) 754-4725

         with a copy to:

         Apollo Management, L.P.
         c/o Joshua Harris
         1301 Avenue of the Americas, 38th Floor
         Telecopier: (212) 515-3263
         Telephone:  (212) 515-3221

         (g) if to the Optionee, to him at his address set forth in the
Company's records or to such other address as the party to whom notice is to be
given may have furnished to the other party in writing in accordance herewith.
Any such notice or communication shall be deemed to have been received (i) in
the case of personal delivery, on the date of such delivery (or if such date is
not a business day, on the next business after the date sent), (ii) in the case
of nationally-recognized overnight courier, on the next business day after the
date sent, (iii) in the case of telecopy transmission, when received (or if not
sent on a business day, on the next business day after the date sent), and (iv)
in the case of mailing, on the third business day following that on which the
piece of mail containing such communication is posted.

9. WAIVER OF BREACH.

         The waiver by either party of a breach of any provision of this
Agreement must be in writing and shall not operate or be construed as a waiver
of any other or subsequent breach.

10. OPTIONEE'S UNDERTAKING.

         The Optionee hereby agrees to take whatever additional actions and
execute whatever additional documents the Company may in its reasonable judgment
deem necessary or advisable in order to carry out or effect one or more of the
obligations or restrictions imposed on the Optionee pursuant to the express
provisions of this Agreement and the Plan.


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<PAGE>

11. MODIFICATION OF RIGHTS.

         Anything contained in this Agreement or the Plan to the contrary
notwithstanding, no provision of this Agreement may be modified or amended
without the prior written consent of the Company and the Optionee, and no
interpretation, modification, amendment or termination of any provision of the
Plan that would adversely affect the rights of the Optionee under or with
respect to the Plan or this Agreement shall be effective as to the Optionee
without the Optionee's prior written consent.

12. GOVERNING LAW.

         All questions concerning the construction, interpretation and validity
of this Agreement shall be governed by and construed and enforced in accordance
with the domestic laws of the State of Florida, without giving effect to any
choice or conflict of law provision or rule (whether in the State of Florida or
any other jurisdiction) that would cause the application of the laws of any
jurisdiction other than the State of Florida. In furtherance of the foregoing,
the internal law of the State of Florida will control the interpretation and
construction of this Agreement, even if under such jurisdiction's choice of law
or conflict of law analysis, the substantive law of some other jurisdiction
would ordinarily apply.

13. COUNTERPARTS.

         This Agreement may be executed in one or snore counterparts, and each
such counterpart shall be deemed to be an original, but all such counterparts
together shall constitute but one agreement.

14. ENTIRE AGREEMENT.

         This Agreement and the Plan (and the other writings referred to herein)
constitute the entire agreement between the parties with respect to the subject
matter hereof and thereof and supersede all prior written or oral negotiations,
commitments, representations and agreements with respect thereto.

                                   * * * * *


<PAGE>

         IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the date written hereunder.

                                    QUALITY DISTRIBUTION, INC.



                                    By:
                                       -----------------------------
                                       Name:
                                       Title:



                                    --------------------------------
                                    Optionee: Doug Allen

EXERCISE PRICE:                                TBD

TOTAL NUMBER OF SHARES:                     10,000
SHARES IN TRANCHE A                          5,000
SHARES IN TRANCHE B                          1,667
SHARES IN TRANCHE C                          1,667
SHARES IN TRANCHE D                          1,666

DATED:    November 19,2000


<PAGE>

                                                                       EXHIBIT 1

                            SUMMARY OF OPTION TERMS

         1. GENERAL. Tranche A Options become vested over time (the "Time
Vesting Options"). Tranche B Options, Tranche C Options, and Tranche D Options
become vested based on certain performance targets (the Performance Options")

         2. TIME VESTING OPTIONS. 25% of the Time Vesting Options shall become
Vested Options on December 31, 2001, an additional 25% shall become vested on
each of the three anniversaries of December 31, 2001 if the Executive is
employed by the Company on each of such dates.

         3. PERFORMANCE VESTING OPTIONS.

         3.1. Vesting. 25% of the options in each tranche become vested on each
Performance Measurement Date, if the Per Share Equity Value exceeds the Per
Share Target Value for a particular tranche.

         3.2. Per Share Target Values. Notwithstanding any provision in the
Plan, the Per Share Target Values for the options granted herein shall be as
follows:

      PERFORMANCE
   MEASUREMENT DATE December 31, 2001 December 31, 2002 December 31, 2003
December 31, 2004

<TABLE>
<CAPTION>
                                            PER SHARE TARGET VALUE
                            ----------------------------------------------------
  PERFORMANCE               TRANCHE               TRANCHE                TRANCHE
MEASUREMENT DATE               B                     C                       D
--------------------------------------------------------------------------------
<S>                         <C>                   <C>                   <C>
December 31, 2001           $  70.00              $  67.50              $  65.00
December 31, 2002              98.00                 91.13                 84.50
December 31, 2003             137.20                123.02                109.85
December 31, 2003           $ 192.08              $ 166.08              $ 142.81
</TABLE>

(* The above Per Share Target Values will finalized upon the determination of
the Per Share Value as of November I, 2000.)

         3.3. Certain Definitions: Notwithstanding any provision in the plan,
the following definitions shall be applied in connection with the Trance B,
Tranche C, and Tranche D Options:

         (a) "PERFORMANCE MEASUREMENT DATE" shall be December 31, 2001, and each
of the three anniversaries thereof.

         (b) "PER SHARE EQUITY VALUE" shall mean, in respect of any Tranche B,
Tranche C or Tranche D Performance Measurement Date, (a) the product of (i)
EBITDA for the twelve-month period ending on such date, multiplied by (ii) 6.5,
plus (b) (i) the aggregate amount of the consolidated cash on hand of the
Company and its subsidiaries plus the aggregate Option Price for all Options
that are "in the money" (as defined below), minus (ii) the liquidation value of
the outstanding consolidated Indebtedness and Company preferred stock (as
adjusted to reflect a Sale of the Company, if applicable, and excluding any debt
or preferred stock associated with an acquisition, the earnings of which are not
included in EBITDA) and minus the amount of cash received by the company in
connection with the settlement of


<PAGE>

environmental claims with the London market and certain other insurers, net of
any environmental expenses paid after December 31, 1999, divided by (c) the sum
of (i) the number of Shares outstanding as of the end of such twelve-month
period and (ii) the number of Shares issuable upon the conversion of securities
convertible into Shares or upon the exercise of options or warrants exercisable
for Shares, in each case in this clause (c), which are "in the money." For
purposes hereof, an option or warrant is "in the money" if the exercise price or
conversion price is less than the Per Share Equity Value, calculated without
giving effect to such convertible securities, options or warrants.
Notwithstanding the foregoing, in the case of a Qualified Public Offering, Per
Share Equity Value shall have the meaning set forth in Sections 7(d), 8(d) and
9(d) of the Plan, as applicable.


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<PAGE>

                                                                       EXHIBIT 2

1998 MTL, INC. OPTION PLAN


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