<PAGE>   1
                                                                     EXHIBIT 4.2

NEITHER THE SECURITIES REPRESENTED BY THIS WARRANT NOR THE SECURITIES INTO
WHICH THIS WARRANT ARE EXERCISABLE HAVE BEEN REGISTERED UNDER THE SECURITIES
ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES LAWS.  THE SECURITIES
HAVE BEEN ACQUIRED FOR INVESTMENT AND MAY NOT BE OFFERED FOR SALE, SOLD,
TRANSFERRED OR ASSIGNED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT
FOR SUCH SECURITIES UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE
STATE SECURITIES LAWS, OR AN OPINION OF COUNSEL, IN FORM AND SUBSTANCE
REASONABLY ACCEPTABLE TO THE COMPANY, THAT REGISTRATION IS NOT REQUIRED UNDER
SAID ACT OR APPLICABLE STATE SECURITIES LAWS OR UNLESS SOLD PURSUANT TO RULE
144 UNDER SAID ACT.  NOTWITHSTANDING THE FOREGOING THIS SECURITY MAY BE PLEDGED
IN CONNECTION WITH A BONA FIDE MARGIN ACCOUNT.


                           QUEEN SAND RESOURCES, INC.

                        WARRANT TO PURCHASE COMMON STOCK

Warrant No.:                                        Number of Shares:          
             ---------------                                         ---------
Date of Issuance: July 8, 1998


Queen Sand Resources, Inc., a Delaware corporation (the "COMPANY"), hereby
certifies that, for value received, ____________________, or its registered
assigns, is entitled, subject to the terms set forth below, to purchase from
the Company upon surrender of this Warrant, at any time or times on or after
the date hereof, but not after 11:59 P.M.  Eastern Time on the Expiration Date
(as defined herein)  ____________________ (_______________) fully paid
nonassessable shares of Common Stock (as defined in Section 1(b)) of the
Company (the "WARRANT SHARES") at the purchase price per share provided in
Section 1(b) below (the "WARRANT EXERCISE PRICE"); provided, however, that in
no event shall the holder be entitled to exercise this Warrant for a number of
Warrant Shares in excess of that number of Warrant Shares which, upon giving
effect to such exercise, would cause the aggregate number of shares of Common
Stock beneficially owned by the holder and its affiliates to exceed 4.99% of
the outstanding shares of the Common Stock following such exercise.  For
purposes of the foregoing proviso, the aggregate number of shares of Common
Stock beneficially owned by the holder and its affiliates shall include the
number of shares of Common Stock issuable upon exercise of this Warrant with
respect to which the determination of such proviso is being made, but shall
exclude shares of Common Stock which would be issuable upon (i) exercise of the
remaining, unexercised Warrants beneficially owned by the holder and its
affiliates and (ii) exercise or conversion of the unexercised or unconverted
portion of any other securities of the Company beneficially owned by the holder
and its affiliates (including, without limitation, any convertible notes,
convertible preferred stock, warrants or rights to receive shares of Common
Stock) subject to a limitation on conversion or exercise analogous to the
limitation contained herein.  Except as set forth in the preceding sentence,
for purposes of this paragraph, beneficial ownership shall be calculated in
accordance with Section
<PAGE>   2
13(d) of the Securities Exchange Act of 1934, as amended.  The holder may waive
the foregoing limitations by written notice to the Company upon not less than
61 days prior notice (with such waiver taking effect only upon the expiration
of such 61 day notice period).

         Section 1.

                 (a)      Securities Purchase Agreement.  This Warrant is one
of the warrants (the "COMMON STOCK WARRANTS") issued pursuant to Section 1 of
that certain Securities Purchase Agreement, dated as of June 25, 1998, among
the Company and the Buyers party thereto, as amended and restated by the
Amended and Restated Securities Purchase Agreement, dated as of July 6, 1998
among the Company and the Buyers party thereto (as amended and restated, the
"PURCHASE AGREEMENT").

                 (b)      Definitions.  The following words and terms as used
in this Warrant shall have the following meanings:

                          "APPROVED STOCK PLAN" shall mean any plan which has
been approved by the Board of Directors of the Company, pursuant to which the
Company's securities may be issued to any employee, officer, director or
consultant for services provided to the Company.

                          "BUSINESS DAY" means any day except Saturday, Sunday
and any day which shall be a legal holiday or a day on which banking
institutions in the State of New York are authorized or required by law or
other government action to close.

                          "CLOSING BID PRICE"  means, for any security as of
any date, the last closing bid price for such security on The Nasdaq SmallCap
Market as reported by Bloomberg Financial Markets ("BLOOMBERG"), or, if The
Nasdaq SmallCap Market is not the principal trading market for such security,
the last closing bid price of such security on a Subsequent Market (as defined
below) on which such security is listed or traded as reported by Bloomberg, or
if the foregoing do not apply, the last closing bid price of such security in
the over-the-counter market on the electronic bulletin board for such security
as reported by Bloomberg, or, if no closing bid price is reported for such
security by Bloomberg, the last closing trade price of such security as
reported by Bloomberg, or, if no last closing trade price is reported for such
security by Bloomberg, the average of the bid prices of any market makers for
such security as reported in the "pink sheets" by the National Quotation
Bureau, Inc.  If the Closing Bid Price cannot be calculated for such security
on such date on any of the foregoing bases, the Closing Bid Price of such
security on such date shall be the fair market value as mutually determined by
the Company and the holders the Common Stock Warrants.  If the Company and the
holders of the Common Stock Warrants are unable to agree upon the fair market
value of the Common Stock, then such dispute shall be resolved pursuant to
Section 2(a) of this Warrant with the term "Closing Bid Price" being
substituted for the term "Market Price."  (All such determinations to be
appropriately adjusted for any stock dividend, stock split or other similar
transaction during such period).





                                      -2-
<PAGE>   3
                          "COMMON STOCK" means (I) the Company's common stock,
par value $.0015 per share, and (ii) any capital stock into which such Common
Stock shall have been changed or any capital stock resulting from a
reclassification of such Common Stock.

                          "COMMON STOCK DEEMED OUTSTANDING" means, at any given
time, the number of shares of Common Stock actually outstanding at such time,
plus the number of shares of Common Stock deemed to be outstanding pursuant to
Sections 8(b)(i) and 8(b)(ii) hereof regardless of whether the Options (as
defined in Section 8(b)(i) below) or Convertible Securities (as defined in
Section 8(b)(i) below) are actually exercisable or convertible at such time,
but excluding any shares of Common Stock issuable upon exercise of the Common
Stock Warrants.

                          "EXPIRATION DATE" means the date three (3) years from
the date of this Warrant or, if such date is not a Business Day, the next
preceding Business Day.

                          "MARKET PRICE" means, with respect to any security
for any date, the average of the Closing Bid Prices for such security during
the five (5) consecutive trading days immediately preceding such date.

                          "OTHER SECURITIES" means (i) those convertible
securities, options and warrants of the Company issued prior to, and
outstanding on, the date of issuance of this Warrant, (ii) the Initial Common
Shares (as defined in the Securities Purchase Agreement), (iii) the Repricing
Common Shares (as defined in the Securities Purchase Agreement), (iv) the
Repricing Rights (as defined in the Securities Purchase Agreement), (v) shares
of Common Stock, and warrants or other securities that are convertible into or
exchangeable for shares of Common Stock, issuable in connection with the
acquisition by the Company of oil and natural gas companies (whether by merger,
purchase of shares or exchange) or properties, and (vi) rights of JEDI (as
defined in the Purchase Agreement) under Section 7.01 of the Securities
Purchase Agreement, dated as of March 27, 1997, between the Company and JEDI
(as such agreement is in effect on the date of the issuance of this Warrant)
arising from any issuances described in clause (v) above in this definition.

                          "PERSON" means an individual, a limited liability
company, a partnership, a joint venture, a corporation, a trust, an
unincorporated organization, a government or any department or agency thereof,
or any other entity or organization.

                          "REGISTRATION RIGHTS AGREEMENT" means the
Registration Rights Agreement dated the date hereof, among the Company and the
Buyers party thereto entered into in connection with the Purchase Agreement.

                          "SECURITIES ACT" means the Securities Act of 1933, as
amended.

                          "SUBSEQUENT MARKET" means any of the New York Stock
Exchange, American Stock Exchange or Nasdaq National Market.





                                      -3-
<PAGE>   4
                          "TRADING DAY" means (a) a day on which the Common
Stock is listed for trading on the Nasdaq SmallCap Market or on a Subsequent
Market or (b) if the Common Stock is not listed on the Nasdaq SmallCap Market
or a Subsequent Market, a day on which the Common Stock is traded in the
over-the-counter market, as reported by the OTC Bulletin Board, or (c) if the
Common Stock is not quoted on the OTC Bulletin Board, a day on which the Common
Stock is quoted in the over-the-counter market as reported by the National
Quotation Bureau Incorporated (or any similar organization or agency succeeding
its functions of reporting prices); provided, however, that in the event that
the Common Stock is not listed or quoted as set forth in (a), (b) and (c)
hereof, then a Trading Day shall be a Business Day.

                          "WARRANT" means this Warrant and all Warrants issued
in exchange, transfer or replacement thereof.

                          "WARRANT EXERCISE PRICE" shall be $7.70, subject to 
adjustment as hereinafter provided.

                 (c)      Other Definitional Provisions.

                          (i)     Except as otherwise specified herein, all
references herein (A) to the Company shall be deemed to include the Company's
successors and (B) to any applicable law defined or referred to herein, shall
be deemed references to such applicable law as the same may have been or may be
amended or supplemented from time to time.

                          (ii)    When used in this Warrant, the words
"HEREIN," "HEREOF," and "HEREUNDER," and words of similar import, shall refer
to this Warrant as a whole and not to any provision of this Warrant, and the
words "SECTION," "SCHEDULE," and "EXHIBIT" shall refer to Sections of, and
Schedules and Exhibits to, this Warrant unless otherwise specified.

                          (iii)   Whenever the context so requires, the neuter
gender includes the masculine or feminine, and the singular number includes the
plural, and vice versa.

         Section 2.       Exercise of Warrant.

                 (a)      Subject to the terms and conditions hereof, this
Warrant may be exercised by the holder hereof then registered on the books of
the Company, in whole or in part, at any time during normal business hours on
any business day on or after the opening of business on the date hereof and
prior to 11:59 P.M. Eastern Time on the Expiration Date by (I) delivery of a
written notice, in the form of the subscription notice attached as Exhibit A
hereto, of such holder's election to exercise this Warrant, which notice shall
specify the number of Warrant Shares to be purchased, (ii) payment to the
Company of an amount equal to the Warrant Exercise Price multiplied by the
number of Warrant Shares as to which the Warrant is being exercised (the
"AGGREGATE EXERCISE PRICE") in cash or by check or wire transfer, and (iii) the
surrender of this Warrant, at the principal office of the Company; provided,
that if such Warrant Shares are to be issued in any name other than that of the
registered holder of this Warrant, such issuance shall be deemed a transfer and
the provisions of Section 7 shall be applicable.  In the event of any





                                      -4-
<PAGE>   5
exercise of the rights represented by this Warrant in compliance with this
Section 2(a), a certificate or certificates for the Warrant Shares so
purchased, in such denominations as may be requested by the holder hereof and
registered in the name of, or as directed by, the holder, shall be delivered at
the Company's expense to, or as directed by, such holder as soon as practicable
after such rights shall have been so exercised, and in any event no later than
three business days after such exercise.  In the case of a dispute as to the
determination of the Warrant Exercise Price of a security or the arithmetic
calculation of the Warrant Shares, the Company shall promptly issue to the
holder the number of shares of Common Stock that is not disputed and shall
submit the disputed determinations or arithmetic calculations to the holder via
facsimile within one business day of receipt of the holder's subscription
notice.  If the holder and the Company are unable to agree upon the
determination of the Warrant Exercise Price or arithmetic calculation of the
Warrant Shares within one day of such disputed determination or arithmetic
calculation being submitted to the holder, then the Company shall immediately
submit via facsimile (I) the disputed determination of the Warrant Exercise
Price to an independent, reputable investment banking firm or (ii) the disputed
arithmetic calculation of the Warrant Shares to its independent, outside
accountant.  The Company shall cause the investment banking firm or the
accountant, as the case may be, to perform the determinations or calculations
and notify the Company and the holder of the results no later than two (2)
Business Days from receipt of the disputed determinations or calculations.
Such investment banking firm's or accountant's determination or calculation, as
the case may be, shall be deemed conclusive absent manifest error.

                 (b)      Unless the rights represented by this Warrant shall
have expired or shall have been fully exercised, the Company shall, as soon as
practicable and in no event later than five business days after any exercise
and at its own expense, issue a new Warrant identical in all respects to the
Warrant exercised except (I) it shall represent rights to purchase the number
of Warrant Shares purchasable immediately prior to such exercise under the
Warrant exercised, less the number of Warrant Shares with respect to which such
Warrant is exercised, and (ii) the holder thereof shall be deemed for all
corporate purposes to have become the holder of record of such Warrant Shares
immediately prior to the close of business on the date on which the Warrant is
surrendered and payment of the amount due in respect of such exercise and any
applicable taxes is made, irrespective of the date of delivery of certificates
evidencing such Warrant Shares, except that, if the date of such surrender and
payment is a date when the stock transfer books of the Company are properly
closed, such person shall be deemed to have become the holder of such Warrant
Shares at the opening of business on the next succeeding date on which the
stock transfer books are open.

                 (c)      No fractional shares of Common Stock are to be issued
upon the exercise of this Warrant, but rather the number of shares of Common
Stock issued upon exercise of this Warrant shall be rounded up or down to the
nearest whole number.

                 (d)      If the Company shall fail for any reason or for no
reason to issue to the holder on a timely basis as described in this Section 2,
a certificate for the number of shares of Common Stock to which the holder is
entitled upon the holder's exercise of this Warrant or a new Warrant for the
number of shares of Common Stock to which such holder is entitled pursuant to
Section 2(b) hereof, the Company shall, in addition to any other remedies under
this Warrant or the Securities Purchase Agreement or otherwise available to
such holder, including





                                      -5-
<PAGE>   6
any indemnification under Section 11 of the Securities Purchase Agreement, pay
as additional damages in cash to such holder on each date after the fifth
business day following receipt by the Company of the exercise notice that such
exercise is not timely effected in an amount equal to 0.5% of the product of
(A) the sum of the number of shares of Common Stock not issued to the holder on
a timely basis and to which the holder is entitled and, in the event the
Company has failed to timely deliver a new Warrant, the number of shares
represented by the portion of this Warrant which is not being converted, as the
case may be, and (B) the average of the Closing Bid Prices for the three
consecutive trading days immediately preceding the last possible date which the
Company could have issued such Common Stock to the holder without violating
this Section 2.

                 (e)  Notwithstanding anything contained herein to the
contrary, the holder of this Warrant may, at its election exercised in its sole
discretion, exercise this Warrant in whole or in part and, in lieu of making
the cash payment otherwise contemplated to be made to the Company upon such
exercise in payment of the Aggregate Exercise Price, elect instead to receive
upon such exercise the "Net Number" of shares of Common Stock determined
according to the following formula:

         Net Number = (A x B) - (A x C)
                      -----------------
                              B

         For purposes of the foregoing formula:

                          A= the total number shares with respect to which this
                          Warrant is then being exercised.

                          B= the Market Price immediately prior to the date of
                          the subscription notice.

                          C= the Warrant Exercise Price then in effect at the
                          time of such exercise.

For purposes of Rule 144 promulgated under the Securities Act, it is intended,
understood and acknowledged that the Warrant Shares issued in a cashless
exercise transaction shall be deemed to have been acquired by the holder
hereof, and the holding period for the Warrant Shares shall be deemed to have
been commenced, on the issue date.

         Section 3.       Covenants as to Common Stock; Certain Registrations.
The Company hereby covenants and agrees as follows:

                 (a)      This Warrant is, and any Common Stock Warrants issued
in substitution for or replacement of this Warrant will upon issuance be, duly
authorized and validly issued.

                 (b)      All Warrant Shares which may be issued upon the
exercise of the rights represented by this Warrant will, upon issuance, be
validly issued, fully paid and nonassessable and free from all taxes, liens and
charges with respect to the issue thereof.





                                      -6-
<PAGE>   7
                 (c)      During the period within which the rights represented
by this Warrant may be exercised, the Company will at all times have authorized
and reserved at least 100% of the number of shares of Common Stock needed to
provide for the exercise of the rights then represented by this Warrant and the
par value of said shares will at all times be less than or equal to the
applicable Warrant Exercise Price.

                 (d)      The Company shall list the Warrant Shares within 10
days of the date of this Warrant on the Nasdaq SmallCap Market and each other
Subsequent Market on which the Common Stock is then listed or traded and shall
maintain such listing for so long as any other shares of Common Stock shall be
so listed.

                 (e)      The Company will not, by amendment of its charter or
through any reorganization, transfer of assets, consolidation, merger,
dissolution, issue or sale of securities, or any other voluntary action, avoid
or seek to avoid the observance or performance of any of the terms to be
observed or performed by it hereunder, but will at all times in good faith
assist in the carrying out of all the provisions of this Warrant.  Without
limiting the generality of the foregoing, the Company (i) will not increase the
par value of any shares of Common Stock receivable upon the exercise of this
Warrant above the Warrant Exercise Price then in effect, and (ii) will take all
such actions as may be necessary or appropriate in order that the Company may
validly and legally issue fully paid and nonassessable shares of Common Stock
upon the exercise of this Warrant.

                 (f)      This Warrant will be binding upon any entity
succeeding to the Company by merger, consolidation or acquisition of all or
substantially all of the Company's assets.

         Section 4.       Taxes.  The Company shall pay any and all taxes which
may be payable with respect to the issuance and delivery of Warrant Shares upon
exercise of this Warrant.

         Section 5.       Warrant Holder Not Deemed a Stockholder.  Except as
otherwise specifically provided herein, no holder, as such, of this Warrant
shall be entitled to vote or receive dividends or be deemed the holder of
shares of the Company for any purpose, nor shall anything contained in this
Warrant be construed to confer upon the holder hereof, as such, any of the
rights of a stockholder of the Company or any right to vote, give or withhold
consent to any corporate action (whether any reorganization, issue of stock,
reclassification of stock, consolidation, merger, conveyance or otherwise),
receive notice of meetings, receive dividends or subscription rights, or
otherwise, prior to the issuance to the holder of this Warrant of the Warrant
Shares which he or she is then entitled to receive upon the due exercise of
this Warrant.  In addition, nothing contained in this Warrant shall be
construed as imposing any liabilities on such holder to purchase any securities
or as a stockholder of the Company, whether such liabilities are asserted by
the Company or by creditors of the Company.  Notwithstanding this Section 5,
the Company will provide the holder of this Warrant with copies of the same
notices and other information given to the stockholders of the Company
generally, contemporaneously with the giving thereof to the stockholders.

         Section 6.       Representations of Holder.  The holder of this
Warrant, by the acceptance hereof, represents that it is acquiring this Warrant
and the Warrant Shares for its own account





                                      -7-
<PAGE>   8
for investment and not with a view to, or for sale in connection with, any
distribution hereof or of any of the shares of Common Stock or other securities
issuable upon the exercise thereof, and not with any present intention of
distributing any of the same.  The holder of this Warrant further represents,
by acceptance hereof, that, as of this date, such holder is an accredited
investor as such term is defined in Rule 501(a) of Regulation D promulgated by
the Securities and Exchange Commission under the Securities Act (an "ACCREDITED
INVESTOR").  Upon exercise of this Warrant, the holder shall, if requested by
the Company, confirm in writing, in a form satisfactory to the Company, that
the Warrant Shares so purchased are being acquired solely for the holder's own
account and not as a nominee for any other party, for investment, and not with
a view toward distribution or resale other than pursuant to an effective
registration statement or an exemption under the Securities Act and that such
holder is an Accredited Investor.  Notwithstanding the foregoing, by making the
representations herein, the holder does not agree to hold the Warrant or the
Warrant Shares for any minimum or other specified term and reserves the right
to dispose of the Warrant and the Warrant Shares at any time in accordance with
or pursuant to a registration statement or an exemption under the Securities
Act.  If such holder cannot make such representations because they would be
factually incorrect, it shall be a condition to such holder's exercise of the
Warrant that the Company receive such other representations as the Company
considers reasonably necessary to assure the Company that the issuance of its
securities upon exercise of the Warrant shall not violate any United States or
state securities laws.

         Section 7.       Ownership and Transfer.

                 (a)      The Company shall maintain at its principal executive
offices (or such other office or agency of the Company as it may designate by
notice to the holder hereof), a register for this Warrant, in which the Company
shall record the name and address of the person in whose name this Warrant has
been issued, as well as the name and address of each transferee.  The Company
may treat the person in whose name any Warrant is registered on the register as
the owner and holder thereof for all purposes, notwithstanding any notice to
the contrary, but in all events recognizing any transfers made in accordance
with the terms of this Warrant.

                 (b)      This Warrant and the rights granted to the holder
hereof are transferable to affiliates of the holder hereof and to any
investment funds that are under common management with such holder, without the
written consent of the Company, and to other Persons, with the consent of the
Company, which consent shall not be unreasonably withheld, in whole or in part,
upon surrender of this Warrant, together with a properly executed warrant power
in the form of Exhibit B attached hereto; provided, however, that any transfer
or assignment shall be subject to the conditions set forth in Section 7(c)
below.

                 (c)      The holder of this Warrant understands that this
Warrant has not been and is not expected to be, registered under the Securities
Act or any state securities laws, and may not be offered for sale, sold,
assigned or transferred unless (a) subsequently registered thereunder, or (b)
such holder shall have delivered to the Company an opinion of counsel,
reasonably satisfactory in form, scope and substance to the Company, to the
effect that the securities to be sold, assigned or transferred may be sold,
assigned or transferred pursuant to an exemption from such registration;
provided that (i) any sale of such securities made in reliance on Rule 144





                                      -8-
<PAGE>   9
promulgated under the Securities Act may be made only in accordance with the
terms of said Rule and further, if said Rule is not applicable, any resale of
such securities under circumstances in which the seller (or the person through
whom the sale is made) may be deemed to be an underwriter (as that term is
defined in the Securities Act) may require compliance with some other exemption
under the Securities Act or the rules and regulations of the Securities and
Exchange Commission thereunder; and (ii) neither the Company nor any other
person is under any obligation to register the Common Stock Warrants under the
Securities Act or any state securities laws or to comply with the terms and
conditions of any exemption thereunder.

                 (d)      The Company is obligated to register the Warrant
Shares for resale under the Securities Act pursuant to the Registration Rights
Agreement and the initial holder of this Warrant (and certain assignees
thereof) is entitled to the registration rights in respect of the Warrant
Shares as set forth in the Registration Rights Agreement.

         Section 8.       Adjustment of Warrant Exercise Price and Number of
Shares.  In order to prevent dilution of the rights granted under this Warrant,
the Warrant Exercise Price and the number of shares of Common Stock issuable
upon exercise of this Warrant shall be adjusted from time to time as follows:

                 (a)      Adjustment of Warrant Exercise Price and Number of
Shares upon Issuance of Common Stock.  If and whenever on or after the date of
issuance of this Warrant, the Company issues or sells, or is deemed to have
issued or sold, any shares of Common Stock or rights, warrants or options
exercisable into or exchangeable for shares of Common Stock (other than shares
of Common Stock deemed to have been issued by the Company in connection with an
Approved Stock Plan or upon exercise of the Other Securities) for a
consideration per share less than a price (the "APPLICABLE PRICE") equal to the
Warrant Exercise Price in effect immediately prior to such issuance or sale,
then immediately after such issue or sale the Warrant Exercise Price shall be
reduced to an amount determined by multiplying the Warrant Exercise Price in
effect immediately prior to such issue or sale by a fraction, the numerator of
which shall be the sum of (i) the number of shares of Common Stock Deemed
Outstanding immediately prior to such issue or sale, and (ii) the number of
shares of Common Stock which the aggregate consideration received (or to be
received, assuming exercise or conversion in full of such rights, warrants or
convertible securities) for the issuance of such additional shares of Common
Stock would purchase at the Warrant Exercise Price, and the denominator of
which shall be the number of shares of Common Stock Deemed Outstanding
immediately after such issue or sale.  Upon each such adjustment of the Warrant
Exercise Price hereunder, the number of shares of Common Stock acquirable upon
exercise of this Warrant shall be adjusted to the number of shares determined
by multiplying the Warrant Exercise Price in effect immediately prior to such
adjustment by the number of shares of Common Stock acquirable upon exercise of
this Warrant immediately prior to such adjustment and dividing the product
thereof by the Warrant Exercise Price resulting from such adjustment.  However,
upon the expiration of any right, warrant or option to purchase shares of
Common Stock the issuance of which resulted in an adjustment in the Warrant
Exercise Price pursuant to this Section, if any such right, warrant or option
shall expire without having been exercised, the Warrant Exercise Price shall,
immediately upon such expiration, be recomputed and effective immediately upon
such expiration shall be increased to the price which it would have been (but
reflecting any other adjustments in the Warrant Exercise





                                      -9-
<PAGE>   10
Price made pursuant to this Warrant upon the issuance of other rights, warrants
or options) had the adjustment of the Warrant Exercise Price made the issuance
of such rights, options or warrants been made on the basis of offering for
subscription or purchase only that number of shares of Common Stock actually
purchased upon the exercise of such rights, options or warrants actually
exercised.

                 (b)      Effect on Warrant Exercise Price of Certain Events.
For purposes of determining the adjusted Warrant Exercise Price under Section
8(a), the following shall be applicable:

                          (i)     Issuance of Options.  If the Company in any
manner grants any rights or options to subscribe for or to purchase Common
Stock (other than pursuant to an Approved Stock Plan or Other Securities) or
any stock or other securities convertible into or exchangeable for, directly or
indirectly, Common Stock (such rights or options being herein called "OPTIONS"
and such convertible or exchangeable stock or securities being herein called
"CONVERTIBLE SECURITIES") and the price per share for which Common Stock is
issuable upon the exercise of such Options or upon conversion or exchange of
such Convertible Securities is less than the Applicable Price, then the total
maximum number of shares of Common Stock issuable upon the exercise of such
Options or upon conversion or exchange of the total maximum amount of such
Convertible Securities issuable upon the exercise of such Options shall be
deemed to be outstanding and to have been issued and sold by the Company for
such price per share.  For purposes of this Section 8(b)(i), the "price per
share for which Common Stock is issuable upon exercise of such Options or upon
conversion or exchange of such Convertible Securities" is determined by
dividing (A) the total amount, if any, received or receivable by the Company as
consideration for the granting of such Options, plus the minimum aggregate
amount of additional consideration payable to the Company upon the exercise of
all such Options, plus in the case of such Options which relate to Convertible
Securities, the minimum aggregate amount of additional consideration, if any,
payable to the Company upon the issuance or sale of such Convertible Securities
and the conversion or exchange thereof, by (B) the total maximum number of
shares of Common Stock issuable upon exercise of such Options or upon the
conversion or exchange of all such Convertible Securities issuable upon the
exercise of such Options. No adjustment of the Warrant Exercise Price shall be
made upon the actual issuance of such Common Stock or of such Convertible
Securities upon the exercise of such Options or upon the actual issuance of
such Common Stock upon conversion or exchange of such Convertible Securities.

                          (ii)    Issuance of Convertible Securities.  If the
Company in any manner issues or sells any Convertible Securities and the price
per share for which Common Stock is issuable upon such conversion or exchange
is less than the Applicable Price, then the maximum number of shares of Common
Stock issuable upon conversion or exchange of such Convertible Securities shall
be deemed to be outstanding and to have been issued and sold by the Company for
such price per share.  For the purposes of this Section 8(b)(ii), the "price
per share for which Common Stock is issuable upon such conversion or exchange"
is determined by dividing (A) the total amount received or receivable by the
Company as consideration for the issue or sale of such Convertible Securities,
plus the minimum aggregate amount of additional consideration, if any, payable
to the Company upon the conversion or exchange thereof, by (B) the total
maximum number of shares of Common Stock issuable upon the conversion or
exchange of all such





                                      -10-
<PAGE>   11
Convertible Securities.  No adjustment of the Warrant Exercise Price shall be
made upon the actual issue of such Common Stock upon conversion or exchange of
such Convertible Securities, and if any such issue or sale of such Convertible
Securities is made upon exercise of any Options for which adjustment of the
Warrant Exercise Price had been or are to be made pursuant to other provisions
of this Section 8(b), no further adjustment of the Warrant Exercise Price shall
be made by reason of such issue or sale.

                          (iii)   Change in Option Price or Rate of Conversion.
If the purchase price provided for in any Options, the additional
consideration, if any, payable upon the issue, conversion or exchange of any
Convertible Securities, or the rate at which any Convertible Securities are
convertible into or exchangeable for Common Stock change at any time, the
Warrant Exercise Price in effect at the time of such change shall be readjusted
to the Warrant Exercise Price which would have been in effect at such time had
such Options or Convertible Securities still outstanding provided for such
changed purchase price, additional consideration or changed conversion rate, as
the case may be, at the time initially granted, issued or sold and the number
of shares of Common Stock acquirable hereunder shall be correspondingly
readjusted; provided that no adjustment shall be made if such adjustment would
result in an increase of the Warrant Exercise Price then in effect.

                 (c)      Effect on Warrant Exercise Price of Certain Events.
For purposes of determining the adjusted Warrant Exercise Price under Sections
8(a) and 8(b), the following shall be applicable:

                          (i)     Calculation of Consideration Received.  If
any Common Stock, Options or Convertible Securities are issued or sold or
deemed to have been issued or sold for cash, the consideration received
therefor will be deemed to be the net amount received by the Company therefor.
In case any Common Stock, Options or Convertible Securities are issued or sold
for a consideration other than cash, the amount of the consideration other than
cash received by the Company will be the fair value of such consideration,
except where such consideration consists of securities, in which case the
amount of consideration received by the Company will be the Market Price of
such securities on the date of receipt.  In case any Common Stock, Options or
Convertible Securities are issued to the owners of the non-surviving entity in
connection with any merger in which the Company is the surviving entity the
amount of consideration therefor will be deemed to be the fair value of such
portion of the net assets and business of the non- surviving entity as is
attributable to such Common Stock, Options or Convertible Securities, as the
case may be.  The fair value of any consideration other than cash or securities
will be determined by the Company's Board of Directors, provided, that, if the
Holder disagrees with such determination, such dispute shall be resolved
promptly by the independent certified public accountants that regularly
examines the financial statements of the Company.

                          (ii)    Treasury Shares.  The number of shares of
Common Stock outstanding at any given time does not include shares owned or
held by or for the account of the Company, and the disposition of any shares so
owned or held will be considered an issue or sale of Common Stock.





                                      -11-
<PAGE>   12
                          (iii)   Record Date.  If the Company takes a record
of the holders of Common Stock for the purpose of entitling them (1) to receive
a dividend or other distribution payable in Common Stock, Options or in
Convertible Securities or (2) to subscribe for or purchase Common Stock,
Options or Convertible Securities, then such record date will be deemed to be
the date of the issue or sale of the shares of Common Stock deemed to have been
issued or sold upon the declaration of such dividend or the making of such
other distribution or the date of the granting of such right of subscription or
purchase, as the case may be.

                          (iv)    Calculations.   All calculations under this
Warrant shall be made to the nearest cent or the nearest 1/100th of a share, as
the case may be.

                 (d)      Adjustment of Warrant Exercise Price upon Subdivision
or Combination of Common Stock.  If the Company at any time after the date of
issuance of this Warrant subdivides (by any stock split, stock dividend,
recapitalization or otherwise) one or more classes of its outstanding shares of
Common Stock into a greater number of shares, the Warrant Exercise Price in
effect immediately prior to such subdivision will be proportionately reduced
and the number of shares of Common Stock obtainable upon exercise of this
Warrant will be proportionately increased.  If the Company at any time after
the date of issuance of this Warrant combines (by combination, reverse stock
split or otherwise) one or more classes of its outstanding shares of Common
Stock into a smaller number of shares, the Warrant Exercise Price in effect
immediately prior to such combination will be proportionately increased and the
number of shares of Common Stock obtainable upon exercise of this Warrant will
be proportionately decreased.

                 (e)      Reorganization, Reclassification, Consolidation,
Merger or Sale.  Any recapitalization, reorganization, reclassification,
consolidation, merger, sale of all or substantially all of the Company's assets
to another Person (as defined below) or other transaction which is effected in
such a way that holders of Common Stock are entitled to receive (either
directly or upon subsequent liquidation) stock, securities or assets with
respect to or in exchange for Common Stock is referred to herein as "ORGANIC
CHANGE."  Prior to the consummation of any Organic Change, the Company will
make appropriate provision (in form and substance satisfactory to the holders
of the Common Stock Warrants representing a majority of the shares of Common
Stock issuable upon exercise of such Common Stock Warrants then outstanding) to
ensure that each of the holders of the Common Stock Warrants will thereafter
have the right to acquire and receive in lieu of or addition to (as the case
may be) the shares of Common Stock immediately theretofore acquirable and
receivable upon the exercise of such holder's Common Stock Warrants, such
shares of stock, securities or assets as may be issued or payable in the
Organic Change with respect to or in exchange for the number of shares of
Common Stock immediately theretofore acquirable and receivable upon the
exercise of such holder's Common Stock Warrants had such Organic Change not
taken place (without taking into account any limitations or restrictions on
exercise).  In any such case, the Company will make appropriate provision (in
form and substance satisfactory to the holders of the Common Stock Warrants
representing a majority of the shares of Common Stock issuable upon exercise of
such Common Stock Warrants then outstanding) with respect to such holders'
rights and interests to insure that the provisions of this Section 8 and
Section 9 will thereafter be applicable to the Common Stock Warrants
(including, in the case of any such consolidation, merger or sale in which the
successor entity or purchasing entity is other than the Company, an immediate
adjustment of the Warrant





                                      -12-
<PAGE>   13
Exercise Price to the value for the Common Stock reflected by the terms of such
consolidation, merger or sale, and a corresponding immediate adjustment in the
number of shares of shares of Common Stock acquirable and receivable upon
exercise of the Common Stock Warrants, if the value so reflected is less than
the Warrant Exercise Price in effect immediately prior to such consolidation,
merger or sale).  The terms of any documents evidencing an Organic Change shall
include such terms as to give effect to the tenor of this provision and
evidencing  the obligation to deliver to each holder of Common Stock Warrants
such shares of stock, securities or assets as, in accordance with the foregoing
provisions, such holder may be entitled to acquire.

                 (f)      Distribution of Assets.  If the Company shall declare
or make any distribution of its assets (or rights to acquire its assets) to
holders of Common Stock as a partial liquidating dividend, by way or return of
capital or otherwise (including any dividend or distribution to the Company's
stockholders of cash or shares (or rights to acquire shares) of capital stock
of a subsidiary) (a "DISTRIBUTION"), at any time after the issuance of this
Warrant, then the holder of this Warrant shall be entitled upon exercise of
this Warrant for the purchase of any or all of the shares of Common Stock
subject hereto, after the record date for determining shareholders entitled to
receive such Distribution, to receive the amount of such assets (or rights)
which would have been payable to the holder had such holder been the holder of
such shares of Common Stock on the record date for determination of
stockholders entitled to such Distribution.

                 (g)      Notices.

                          (i)     Immediately upon any adjustment of the
Warrant Exercise Price, the Company will give written notice thereof to the
holder of this Warrant, setting forth in reasonable detail and certifying the
calculation of such adjustment.

                          (ii)    The Company will give written notice to the
holder of this Warrant at least twenty (20) days prior to the date on which the
Company closes its books or takes a record (A) with respect to any dividend or
distribution upon the Common Stock, (B) with respect to any pro rata
subscription offer to holders of Common Stock or (C) for determining rights to
vote with respect to any Organic Change, dissolution or liquidation and in no
event shall such notice be provided to such holder prior to such information
being made known to the public.

                          (iii)   The Company will also give written notice to
the holder of this Warrant at least twenty (20) days prior to the date on which
any Organic Change, dissolution or liquidation will take place and in no event
shall such notice be provided to such holder prior to such information being
made known to the public.

         Section 9.       Purchase Rights.  In addition to any adjustments
pursuant to Section 8 above, if at any time the Company grants, issues or sells
any Options, Convertible Securities or rights to purchase stock, warrants,
securities or other property pro rata to the record holders of Common Stock
(the "PURCHASE RIGHTS"), then the holder of this Warrant will be entitled to
acquire, upon the terms applicable to such Purchase Rights, the aggregate
Purchase Rights which such holder could have acquired if such holder had held
the number of shares of Common Stock acquirable upon complete exercise of this
Warrant immediately before the date on which a record is taken for the grant,
issuance or sale of such Purchase Rights, or, if no such record is taken,





                                      -13-
<PAGE>   14
the date as of which the record holders of Common Stock are to be determined
for the grant, issue or sale of such Purchase Rights.

         Section 10.      Lost, Stolen, Mutilated or Destroyed Warrant.  If
this Warrant is lost, stolen, mutilated or destroyed, the Company shall, on
receipt of an indemnification undertaking, issue a new Warrant of like
denomination and tenor as the Warrant so lost, stolen, mutilated or destroyed.

         Section 11.      Notice.  Any notices, consents, waivers or other
communications required or permitted to be given under the terms of this
Warrant must be in writing and will be deemed to have been delivered (I) upon
receipt, when delivered personally; (ii) upon receipt, when sent by facsimile
(provided confirmation of transmission is mechanically or electronically
generated and kept on file by the sending party); or (iii) upon receipt, when
delivered by a delivery service, in each case properly addressed to the party
to receive the same.  The addresses and facsimile numbers for such
communications shall be:

                 If to the Company:

                          Queen Sand Resources, Inc.
                          3500 Oak Lawn, Suite 380, LB#31
                          Dallas, Texas 75219
                          Telephone:       214-521-9955
                          Facsimile:       214-521-9960
                          Attention:       Robert P. Lindsay

                 and

                          Queen Sand Resources, Inc.
                          30 Metcalfe Street, Suite 620
                          Ottawa, Ontario, Canada K1P 5L4
                          Telephone:       613-230-7211
                          Facsimile:       613-230-6055
                          Attention:       Edward J. Munden

                 With copy to:

                          Haynes and Boone, LLP
                          901 Main Street, Suite 3100
                          Dallas, Texas 75202
                          Telephone:       (214) 651-5553
                          Facsimile:       (214) 651-5940
                          Attention:       William L. Boeing, Esq.

                 If to a holder of this Warrant, to it at the address set forth
                 below such holder's signature on the signature page hereof.





                                      -14-
<PAGE>   15
Each party shall provide five days' prior written notice to the other party of
any change in address or facsimile number.

         Section 12.      Miscellaneous.  This Warrant and any term hereof may
be changed, waived, discharged, or terminated only by an instrument in writing
signed by the party or holder hereof against which enforcement of such change,
waiver, discharge or termination is sought.  The headings in this Warrant are
for convenience of reference only and shall not limit or otherwise affect the
meaning hereof.  This Warrant shall be governed by and interpreted under the
laws of the State of New York without regard to principles of conflicts of law
thereof.


                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK,
                            SIGNATURE PAGE FOLLOWS]





                                      -15-
<PAGE>   16
                 IN WITNESS WHEREOF, the Company has cause this Warrant to be
duly executed by its duly authorized officer as of the date first indicated
above.


                                       QUEEN SAND RESOURCES, INC.
                                       
                                       
                                       
                                       By:                                   
                                          -----------------------------------
                                                                             
                                       Name:                                 
                                             --------------------------------
                                                                             
                                       Title:                                
                                              -------------------------------
<PAGE>   17
                              EXHIBIT A TO WARRANT

                               SUBSCRIPTION FORM
        TO BE EXECUTED BY THE REGISTERED HOLDER TO EXERCISE THIS WARRANT
                                        QUEEN SAND RESOURCES, INC.
         The undersigned holder hereby exercises the right to purchase
_________________ of the shares of Common Stock ("WARRANT SHARES") of Queen
Sand Resources, Inc., a Delaware corporation (the "COMPANY"), evidenced by the
attached Warrant (the "WARRANT").  Capitalized terms used herein and not
otherwise defined shall have the respective meanings set forth in the Warrant.

         1.  Form of Warrant Exercise Price.  The Holder intends that payment
of the Warrant Exercise Price shall be made as:

                              a "Cash Exercise" with respect to ____________
                 ----------   Warrant Shares; and/or                       
                           
                              a "Cashless Exercise" with respect to ___________
                 ----------   Warrant Shares (to the extent permitted by the
                              terms of the Warrant).

         2.  Payment of Warrant Exercise Price.  In the event that the holder
has elected a Cash Exercise with respect to some or all of the Warrant Shares
to be issued pursuant hereto, the holder shall pay the sum of
$___________________ to the Company in accordance with the terms of the
Warrant.

         3.  Delivery of Warrant Shares.  The Company shall deliver to the
holder __________ Warrant Shares in accordance with the terms of the Warrant.



Date:                           ,
     -------------------- ------  ---------

                                           
-------------------------------------------
   Name of Registered Holder

By:                                        
         ----------------------------------
         Name:
         Title:
<PAGE>   18
                              EXHIBIT B TO WARRANT

                             FORM OF WARRANT POWER


FOR VALUE RECEIVED, the undersigned does hereby assign and transfer to
________________, Federal Identification No.  __________, a warrant to purchase
____________ shares of the capital stock of Queen Sand Resources, Inc., a
Delaware corporation, represented by warrant certificate no. _____, standing in
the name of the undersigned on the books of said corporation.  The undersigned
does hereby irrevocably constitute and appoint ______________, attorney to
transfer the warrants of said corporation, with full power of substitution in
the premises.


Dated: 
      ---------------------


                                            -------------------------------

                                            By:
                                                 --------------------------
                                            Its: 
                                                 --------------------------
<PAGE>   19
                                   SCHEDULE A


<TABLE>
<CAPTION>
Name                                                   Number of Warrants
----                                                   ------------------
<S>                                                         <C>
JNC Opportunity Fund, Ltd.                                  121,500

JNC Opportunity Fund, Ltd.                                  243,000

Jesup & Lamont Securities Corporation
  and other placement agents                                400,000

Diversified Strategies Fund                                   7,000

Diversified Strategies Fund                                   3,500

Canadian Advantages, L.P.                                    10,000

Sovereign Partners L.P.                                      80,000

Dominion Capital Fund, Ltd.                                  50,000

Advantage (Bermuda) Fund, Ltd.                               10,000

CSM GmbH                                                     80,000
</TABLE>