<PAGE>   1
                                                                 EXHIBIT 10.4

                                MOBILE MINI, INC.
                             1999 STOCK OPTION PLAN


Section 1.        PURPOSE OF PLAN

                  The purposes of the Mobile Mini, Inc. 1999 Stock Option Plan
(the "Plan") are to attract and retain the best available personnel for
positions of substantial responsibility, and to provide an incentive to, and to
encourage ownership of the stock of Mobile Mini, Inc. ("Company"), by its key
management and other employees. Options granted under the Plan may be Incentive
Stock Options within the meaning of Section 422 of the Internal Revenue Code
(the "Code") or nonstatutory stock options, as determined by the Committee at
the time of grant.

Section 2.        STOCK SUBJECT TO THE PLAN

                  (a) Stock Available for Grants of Options. Subject to the
provisions of Section 14, 500,000 shares of the Common Stock, par value $.01 per
share, of the Company ("Common Stock") have been allocated to the Plan and
reserved for issuance upon the exercise of options granted under the Plan.

                  (b) Treasury Shares. The Company may, in its discretion, use
shares held in the treasury under this Plan in lieu of authorized but unissued
shares of Common Stock. If any option shall expire or terminate for any reason
without having been exercised in full, the unpurchased shares subject thereto
shall again be available for the purposes of the Plan. Any shares of Common
Stock which are used as full or partial payment to the Company by an optionee of
the purchase price upon exercise of the option shall again be available for the
purposes of the Plan.

Section 3.        ADMINISTRATION

                 The Plan shall be administered by the Committee referred to in
Section 4 (the "Committee"). Subject to the provisions of the Plan, the
Committee shall have plenary authority, in its discretion, to determine the
individuals to whom, and the time or times at which, options shall be granted
and the number of shares to be subject to each option. In making such
determinations the Committee may take into account the nature of the services
rendered by the respective individuals, their present and potential
contributions to the Company's success and such other factors as the Committee,
in its discretion, shall deem relevant. Subject to the express provisions of the
Plan, the Committee shall also have plenary authority to interpret the Plan, to
prescribe, amend and rescind rules and regulations relating to it, to determine
the terms and provisions of the options (which need not be identical) and to
make all other determinations necessary or advisable for the administration of
the Plan. The Committee shall have authority to determine the terms and
provisions of option agreements evidencing the options granted pursuant to the
Plan, which may vary from the provisions set forth in any form of option
agreement adopted from time to time by the Committee or the Board of Directors.
The Committee's determinations on the matters referred to in this Section 3
shall be conclusive. The Committee may, in its discretion, delegate to the Chief
Executive Officer of the Company (the "CEO") the
<PAGE>   2
authority to determine the individuals to whom, and the time or times at which
and terms upon which, options shall be granted and the number of shares to be
subject to each option; provided, however, that the Committee may not delegate
such authority to the CEO with respect to employees of the Company who are
subject to the reporting requirements of Section 16(a) of the Securities
Exchange Act of 1934.

Section 4.        THE COMMITTEE

                  The Plan shall be administered by a committee (the
"Committee") which shall at all times be constituted to comply with Rule 16b-3
under the Securities Exchange Act of 1934, or any successor Rule. Subject to the
foregoing, the Compensation Committee of the Board of Directors of the Company
("Board") shall be the Committee hereunder.

Section 5.        ELIGIBILITY

                  Options (including Incentive Stock Options) may be granted
only to employees of the Company or its subsidiaries (as defined below). For the
purposes of this Plan, the term "employees" does not include directors who are
not also employees of the Company or a subsidiary. The term "subsidiary" shall
mean any corporation (other than the Company) in an unbroken chain of
corporations beginning with the Company if, at the time of the granting of the
option, each of the corporations other than the last corporation in the unbroken
chain owns stock possessing 50% or more of the total combined voting power of
all classes of stock in one of the other corporations in such chain, or such
other meaning as may be hereafter ascribed in it in Section 424 of the Code.

                  Notwithstanding the foregoing, options which are not Incentive
Stock Options may also be granted to employees of joint ventures of the Company
so long as such employees are not subject to Section 16(a) of the Securities
Exchange Act of 1934 by virtue of their position with, or share holdings of, the
Company. The term "joint venture" means a partnership or other business entity
(other than a subsidiary) 50% or more of the profits interest of which is owned
by the Company or a subsidiary.

Section 6.        OPTION PRICES

                  The purchase price of the Common Stock under each Incentive
Stock Option or other option shall not be less than 100% of the fair market
value of the stock at the time of granting of the option. Such fair market value
shall generally be considered to be the mean between the high and low prices of
the Company's Common Stock as reported by The Nasdaq Stock Market for the day
the option is granted; provided, however, that the Committee may adopt any other
criterion for the determination of such fair market value as it may determine to
be appropriate.

Section 7.        PAYMENT OF OPTION PRICES

                  The purchase price is to be paid in full upon the exercise of
the option, either (i) in cash, (ii) in the discretion of the Committee, by the
tender to the Company of shares of the Common Stock of the Company, owned by the
optionee and registered in the optionee's name,







                                       2
<PAGE>   3
having a fair market value equal to the cash exercise price of the option being
exercised, with the fair market value of such stock to be determined in such
appropriate manner as may be provided for by the Committee or as may be required
in order to comply with, or to conform to the requirements of, any applicable
laws or regulations, or (iii) in the discretion of the Committee, by any
combination of the payment methods specified in clauses (i) and (ii) hereof.
Provided, however, that no shares of Common Stock may be tendered in exercise of
an option if such shares were acquired by the optionee through the exercise of
an Incentive Stock Option unless (i) such shares have been held by the optionee
for at least one year and (ii) at least two years have elapsed since such
Incentive Stock Option was granted. The cash proceeds of sale of stock subject
to option are to be added to the general funds of the Company and used for its
general corporate purposes. The shares of Common Stock of the Company received
by the Company as payment of the option price are to be added to the shares of
the Common Stock of the Company held in its Treasury and used for the purposes
of granting options under the Plan or as the Board shall otherwise determine.

Section 8.        OPTION AMOUNTS

                  The maximum aggregate fair market value (determined at the
time an option is granted in the same manner as provided for in Section 6
hereof) of the Common Stock of the Company with respect to which Incentive Stock
Options are exercisable for the first time by any optionee during any calendar
year (under all plans of the Company and its subsidiaries) shall not exceed
$100,000. The maximum number of shares of Common Stock with respect to which
options under the Plan may be granted to any single person during any three year
period shall be 50% of all shares reserved for issuance pursuant to the Plan.

Section 9.        EXERCISE OF OPTIONS

                  The term of each option shall be not more than ten (10) years
from the date of granting thereof or such shorter period as is prescribed in
Section 10 hereof. Within such limit, options will be exercisable at such time
or times, and subject to such restrictions and conditions, as the Committee
shall, in each instance, approve, which need not be uniform for all optionees;
provided, however, that except as provided in Sections 10 and 11 hereof, no
option may be exercised at any time unless the optionee is then an employee of
the Company or a subsidiary or joint venture and has been so employed
continuously since the granting of the option. The holder of an option shall
have none of the rights of a stockholder with respect to the shares subject to
option until such shares shall be issued to such holder upon the exercise of the
option.

Section 10.       TERMINATION OF EMPLOYMENT

                  The holder of any option issued hereunder must exercise the
option prior to the holder's termination of employment with the Company, a
subsidiary or a joint venture, except that the Committee in its absolute
discretion (exercised at the time of grant or thereafter) may permit the
optionee to exercise the option, to the extent that the holder was entitled to
exercise it at the date of such termination of employment, at any time within
three (3) months after such termination, but not after ten (10) years from the
date the option was granted. If the holder of an option terminates employment on
account of disability, the holder may exercise such option to the






                                       3
<PAGE>   4
extent the holder was entitled to exercise it at the date of such termination at
any time within one (1) year of the termination of employment but not after ten
(10) years from the date the option was granted. For this purpose a person shall
be deemed to be disabled if he or she is permanently and totally disabled within
the meaning of Section 422(c)(6) of the Code, which, as of the date hereof,
means that he or she is unable to engage in any substantial gainful activity by
reason of any medically determined physical or mental impairment which can be
expected to result in death or which has lasted or can be expected to last for a
period of not less than 12 months. A person shall be considered disabled only if
he or she furnishes such proof of disability as the Committee may require.
Options granted under the Plan shall not be affected by any change of employment
so long as the holder continues to be an employee of the Company or a subsidiary
or joint venture thereof. The option agreements may contain such provisions as
the Committee shall approve with reference to the effect of approved leaves of
absence. Nothing in the Plan or in any option granted pursuant to the Plan shall
confer on any individual any right to continue in the employ of the Company or
any subsidiary or joint venture or interfere in any way with the right of the
Company or any subsidiary or joint venture thereof to terminate his or her
employment at any time.

Section 11.       DEATH

                  In the event of the death of an individual to whom an option
has been granted under the Plan, while he or she is employed by the Company (or
a subsidiary or joint venture) or within three (3) months after termination of
employment (or one (1) year in the case of the termination of employment of an
option holder who is disabled as above provided) the option theretofore granted
may be exercised, to the extent exercisable at the date of death, by a legatee
or legatees under the option holder's last will, or by personal representatives
or distributees, at any time within a period of one (1) year after death, but
not after ten (10) years from the date of granting thereof, and only if and to
the extent that the option was exercisable at the date of death.

Section 12.       NON-TRANSFERABILITY OF OPTIONS

                  Each option granted under the Plan shall, by its terms, be
non-transferable otherwise than by will or the laws of descent and distribution
and an option may be exercised, during the lifetime of the holder thereof, only
by such holder. Notwithstanding the foregoing, the Committee in its discretion
may allow options to be transferred to an optionee's "family member" as that
term is defined in the General Instructions to Form S-8 as adopted from time to
time by the Securities and Exchange Commission or any successor to such
commission.

Section 13.       SUCCESSIVE OPTION GRANTS

                  Successive option grants may be made to any holder of options
under this Plan.

Section 14.       ADJUSTMENTS UPON CHANGES IN CAPITALIZATION OR CORPORATE
ACQUISITIONS

                  Notwithstanding any other provisions of the Plan, the option
agreements may contain such provisions as the Committee shall determine to be
appropriate for the adjustment of the number and class of shares subject to each
outstanding option, the option prices in the event







                                       4
<PAGE>   5
of changes in the outstanding Common Stock by reason of stock dividends,
recapitalizations, mergers, consolidations, spin-offs, split-offs, split-ups,
combinations or exchanges of shares and the like, and, in the event of any such
change in the outstanding Common Stock, the aggregate number and class of shares
available under the Plan and the maximum number of shares as to which options
may be granted to any individual shall be appropriately adjusted by the
Committee, whose determination shall be conclusive. In the event the Company or
a subsidiary enters into a transaction described in Section 424(a) of the Code
with any other corporation, the Committee may grant options to employees or
former employees of such corporation in substitution of options previously
granted to them upon such terms and conditions as shall be necessary to qualify
such grant as a substitution described in Section 424(a) of the Code.

Section 15.       AMENDMENT AND TERMINATION

                  The Board or the Committee may at any time terminate the Plan,
or make such modifications of the Plan as they shall deem advisable, provided,
however, that the Board or Committee may not, without the approval by the
stockholders of the Company by act of the stockholders at a meeting held for the
purpose, make any modifications which, under applicable law, require such
approval. No termination or amendment to the Plan may, without the consent of
the optionee to whom any option shall theretofore have been granted, adversely
affect the rights of such optionee under such option.

Section 16.       EFFECTIVENESS OF THE PLAN

                  The Plan became effective upon adoption by the Board on August
17, 1999 subject, however, to its further approval by the stockholders of the
Company on or before August 16, 2000.

Section 17.       TIME OF GRANTING OF OPTIONS

                  An option grant under the Plan shall be deemed to be made on
the date on which the Committee, by formal action of its members duly recorded
in the records thereof, or the CEO, as the case may be, makes an award of an
option to an eligible employee of the Company or one of its subsidiaries
provided that such option is evidenced by a written option agreement duly
executed on behalf of the Company and on behalf of the optionee within a
reasonable time after the date of the Committee or CEO action.

Section 18.       TERM OF PLAN

                  This Plan shall terminate ten (10) years after the date on
which it was initially approved and adopted by the Board as set forth under
Section 16 and no option shall be granted hereunder after the expiration of such
ten-year period. Options outstanding at the termination of the Plan shall
continue in full force and effect and shall not be affected thereby.





                                       5