3,400,000 Shares

Exhibit 1.1

3,400,000 Shares

Myriad Genetics, Inc.

COMMON STOCK, $0.01 par value

UNDERWRITING AGREEMENT

June 3, 2004

Morgan Stanley & Co. Incorporated

1585 Broadway

New York, New York 10036

Dear Sirs and Mesdames:

Myriad Genetics, Inc., a Delaware corporation (the “Company”), proposes to issue and sell to Morgan Stanley & Co. Incorporated (the “Underwriter”) 3,400,000 shares of its common stock, $0.01 par value per share (the “Firm Shares”). The Company also proposes to issue and sell to the Underwriter not more than an additional 510,000 shares of its common stock, $0.01 par value per share (the “Additional Shares”), if and to the extent that you shall have determined to exercise the right to purchase such shares of common stock granted to you in Section 2 hereof. The Firm Shares and the Additional Shares are hereinafter collectively referred to as the “Shares.” The shares of common stock, $0.01 par value per share, of the Company to be outstanding after giving effect to the sales contemplated hereby are hereinafter referred to as the “Common Stock.”

The Company has filed with the Securities and Exchange Commission (the “Commission”) in accordance with the provisions of the Securities Act of 1933, as amended (the “Securities Act”), and the rules and regulations of the Commission thereunder, including Rule 415 thereunder, a registration statement (No. 333-73124) on Form S-3, including a prospectus, for the registration of the Shares (and certain other securities). The term “Registration Statement” means such registration statement, including the exhibits thereto, as amended to the date of this Agreement. The term “Base Prospectus” means the prospectus included in the Registration Statement. If the Company has filed or files an abbreviated registration statement to register additional shares of Common Stock pursuant to Rule 462(b) (the “Rule 462 Registration Statement”) under the Securities Act, then any reference herein to the term “Registration Statement” shall be deemed to include such Rule 462 Registration Statement.

The Company has filed with, or transmitted for filing to, or shall promptly hereafter file with or transmit for filing to, the Commission a prospectus supplement (the “Prospectus Supplement”) specifically relating to the Shares, pursuant to Rule 424 under the Securities Act. The term “Prospectus” means the Prospectus Supplement together with the Base Prospectus. As used herein, the terms “Base Prospectus,” “Prospectus” and “Registration Statement” shall include in each case the documents, if any, incorporated or deemed to be incorporated by reference therein (it being

understood that any statement contained in a document incorporated or deemed to be incorporated by reference in the Base Prospectus, Prospectus Supplement or Registration Statement, or any supplements or amendments to any of such documents, shall not be deemed to constitute a part thereof to the extent modified or superseded by a statement contained in any subsequently filed document which also is or is deemed to be incorporated by reference therein). The terms “supplement” and “amendment” or “amend” as used in this Agreement shall include all documents filed subsequent to the date of the Base Prospectus, as the case may be, by the Company with the Commission pursuant to the Securities Exchange Act of 1934, as amended (the “Exchange Act”), that are deemed to be incorporated by reference in the Prospectus.

1. Representations and Warranties.

The Company represents and warrants to and agrees with the Underwriter that:

(a) The Registration Statement has become effective; no stop order suspending the effectiveness of the Registration Statement is in effect, and no proceedings for such purpose are pending before or threatened by the Commission.

(b) (i) The Registration Statement, when it became effective, did not contain and, as amended or supplemented, if applicable, will not contain any untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary to make the statements therein not misleading, (ii) the Registration Statement and the Prospectus comply as to form and, as amended or supplemented, if applicable, will comply as to form in all material respects with the Securities Act and the applicable rules and regulations of the Commission thereunder and (iii) the Prospectus does not contain and, as amended or supplemented, if applicable, will not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements therein, in the light of the circumstances under which they were made, not misleading, except that the representations and warranties set forth in this paragraph do not apply to statements or omissions in the Registration Statement or the Prospectus based upon information relating to the Underwriter furnished to the Company in writing by the Underwriter expressly for use therein.

(c) The Company has been duly incorporated, is validly existing as a corporation in good standing under the laws of the jurisdiction of its incorporation, has the corporate power and authority to own its property and to conduct its business as described in the Prospectus and is duly qualified to transact business and is in good standing in each jurisdiction in which the conduct of its business or its ownership or leasing of property requires such qualification, except to the extent that the failure to be so qualified or be in good standing would not have a material adverse effect on the Company and its subsidiaries, taken as a whole.

(d) Each subsidiary of the Company has been duly incorporated, is validly existing as a corporation in good standing under the laws of the jurisdiction of its incorporation, has the corporate power and authority to own its property and to conduct its business as described in the Prospectus and is duly qualified to transact business and is in good standing in each jurisdiction in which the conduct of its business or its ownership or leasing of property requires such qualification, except to the extent that the failure to be so qualified or be in good standing would not have a

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material adverse effect on the Company and its subsidiaries, taken as a whole; all of the issued shares of capital stock of each subsidiary of the Company have been duly authorized and validly issued, are fully paid and non-assessable and are owned directly by the Company, free and clear of all liens, encumbrances, equities or claims.

(e) This Agreement has been duly authorized, executed and delivered by the Company.

(f) The authorized capital stock of the Company conforms as to legal matters to the description thereof contained in the Prospectus.

(g) The shares of Common Stock outstanding prior to the issuance of the Shares have been duly authorized and are validly issued, fully paid and non-assessable.

(h) The Shares have been duly authorized and, when issued and delivered in accordance with the terms of this Agreement, will be validly issued, fully paid and non-assessable, and the issuance of such Shares will not be subject to any preemptive or similar rights.

(i) The execution and delivery by the Company of, and the performance by the Company of its obligations under, this Agreement will not contravene any provision of applicable law or the certificate of incorporation or bylaws of the Company or any agreement or other instrument binding upon the Company or any of its subsidiaries that is material to the Company and its subsidiaries, taken as a whole, or any judgment, order or decree of any governmental body, agency or court having jurisdiction over the Company or any subsidiary, and no consent, approval, authorization or order of, or qualification with, any governmental body or agency is required for the performance by the Company of its obligations under this Agreement, except such as may be required by the securities or Blue Sky laws of the various states or foreign jurisdictions in connection with the offer and sale of the Shares and required notices of the issuances of the Shares to The Nasdaq National Market.

(j) There has not occurred any material adverse change, or any development involving a prospective material adverse change, in the condition, financial or otherwise, or in the earnings, business or operations of the Company and its subsidiaries, taken as a whole, from that set forth in the Prospectus (exclusive of any amendments or supplements thereto subsequent to the date of this Agreement).

(k) There are no legal or governmental proceedings pending or threatened to which the Company or any of its subsidiaries is a party or to which any of the properties of the Company or any of its subsidiaries is subject that are required to be described in the Registration Statement or the Prospectus and are not so described or any statutes, regulations, contracts or other documents that are required to be described in the Registration Statement or the Prospectus or to be filed as exhibits to the Registration Statement that are not described or filed as required.

(l) The Company is not and, after giving effect to the offering and sale of the Shares and the application of the proceeds thereof as described in the Prospectus, will not be required to register as an “investment company” as such term is defined in the Investment Company Act of 1940, as amended.

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(m) The Company and its subsidiaries (i) are in compliance with any and all applicable foreign, federal, state and local laws and regulations relating to the protection of human health and safety, the environment or hazardous or toxic substances or wastes, pollutants or contaminants (“Environmental Laws”), (ii) have received all permits, licenses or other approvals required of them under applicable Environmental Laws to conduct their respective businesses and (iii) are in compliance with all terms and conditions of any such permit, license or approval, except where such noncompliance with Environmental Laws, failure to receive required permits, licenses or other approvals or failure to comply with the terms and conditions of such permits, licenses or approvals would not, singly or in the aggregate, have a material adverse effect on the Company and its subsidiaries, taken as a whole.

(n) There are no costs or liabilities associated with the Company’s compliance with Environmental Laws (including, without limitation, any capital or operating expenditures required for clean-up, closure of properties or compliance with Environmental Laws or any permit, license or approval, any related constraints on operating activities and any potential liabilities to third parties) which would, singly or in the aggregate, have a material adverse effect on the Company and its subsidiaries, taken as a whole.

(o) There are no contracts, agreements or understandings between the Company and any person granting such person the right to require the Company to file a registration statement under the Securities Act with respect to any securities of the Company or to require the Company to include such securities with the Shares registered pursuant to the Registration Statement.

(p) The Company, at the time the Registration Statement was filed, and at all times subsequent thereto, to and including the Closing Date, qualified and will qualify for use of Form S-3 under the Securities Act for the offer and sale of the Shares pursuant to the standards for Form S-3 effective prior to October 21, 1992 for offerings pursuant to Rule 415 of the Securities Act.

(q) The Company is not aware of any failure on the part of the Company’s chief executive officer or chief financial officer to comply with the certification requirements (collectively, the “Certifications”) of Sections 302 and 906 of the Sarbanes-Oxley Act of 2002 and the rules and regulations promulgated thereunder (the “SOX Act”), in connection with the Certifications that were required to be filed or submitted with the Company’s Annual Report on Form 10-K for the year ended June 30, 2003, and its Quarterly Reports on Form 10-Q for the quarters ended September 30, 2003, December 31, 2003 and March 31, 2004. In addition, the Company is not currently aware of any reason why the Company’s chief executive officer and chief financial officer will be unable to comply with the Certification requirements in connection with the Company’s Annual Report on Form 10-K for the year ending June 30, 2004. There is and has been no failure on the part of the Company, or to the Company’s knowledge, any of the Company’s directors or officers, in their capacities as such, to comply in all material respects with Section 402 of the SOX Act, since the date on which such act took effect.

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(r) The Company believes that, based on preclinical and clinical data known to the Company and other reasonable assumptions that it has relied on in establishing the size of the total patient group enrolled in the Company’s ongoing Phase II/III clinical trial of Flurizan for the treatment of prostate cancer (the “Prostate Cancer Trial”), the current level of patient enrollment in the Prostate Cancer Trial (taking into account the anticipated rate of future patient dropouts), should be adequate to lead to statistically significant results for the primary endpoint of such study as described in the Registration Statement and Prospectus.

2. Agreements to Sell and Purchase. The Company hereby agrees to sell to the Underwriter, and the Underwriter, upon the basis of the representations and warranties herein contained, but subject to the conditions hereinafter stated, agrees to purchase from the Company 3,400,000 Shares at $14.75 a share (the “Purchase Price”).

On the basis of the representations and warranties contained in this Agreement, and subject to its terms and conditions, the Company agrees to sell to you the Additional Shares, and you shall have the right to purchase up to 510,000 Additional Shares at the Purchase Price. You may exercise this right in whole or from time to time in part by giving written notice of each election to exercise the option not later than 30 days after the date of this Agreement. Any exercise notice shall specify the number of Additional Shares to be purchased by you and the date on which such shares are to be purchased. Each purchase date must be at least one business day after the written notice is given and may not be earlier than the Closing Date nor later than ten business days after the date of such notice. Additional Shares may be purchased as provided in Section 4 hereof solely for the purpose of covering over-allotments made in connection with the offering of the Firm Shares.

The Company hereby agrees that, without the prior written consent of the Underwriter, it will not, during the period ending 90 days after the date of the Prospectus, (i) offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, lend, or otherwise transfer or dispose of, directly or indirectly, any shares of Common Stock or any securities convertible into or exercisable or exchangeable for Common Stock or (ii) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of the Common Stock, whether any such transaction described in clause (i) or (ii) above is to be settled by delivery of Common Stock or such other securities, in cash or otherwise. The foregoing sentence shall not apply to (A) the Shares to be sold hereunder or (B) the issuance by the Company of shares of Common Stock upon the exercise of an option or warrant or the conversion of any securities, or the grant by the Company of options to purchase shares of Common Stock under any equity compensation plan existing on the date hereof, as disclosed in the Registration Statement or the Prospectus, in the ordinary course of business consistent with past practice.

3. Terms of Public Offering. The Company is advised by you that you propose to make a public offering of the Shares as soon after this Agreement has become effective as in your judgment is advisable. The Company is further advised by you that the Shares are to be offered to the public initially at $15.25 a share (the “Public Offering Price”).

4. Payment and Delivery. Payment for the Firm Shares shall be made to the Company in Federal or other funds immediately available in New York City against delivery of such Firm Shares for the account of the Underwriter at 10:00 a.m., New York City time, on June 9, 2004, or at such other time on the same or such other date, not later than June 9, 2004, as shall be designated in writing by you. The time and date of such payment are hereinafter referred to as the “Closing Date.”

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Payment for any Additional Shares shall be made to the Company in Federal or other funds immediately available in New York City against delivery of such Additional Shares for the account of the Underwriter at 10:00 a.m., New York City time, on the date specified in the corresponding notice described in Section 2 or at such other time on the same or on such other date, in any event not later than July 16, 2004, as shall be designated in writing by you. The time and date of such payment are hereinafter referred to as the “Option Closing Date.” In no event shall the date of such payment be later than the Option Closing Date.

Certificates for the Firm Shares and Additional Shares shall be in definitive form and registered in such names and in such denominations as you shall request in writing not later than one full business day prior to the Closing Date or the Option Closing Date, as the case may be. The certificates evidencing the Firm Shares and the Additional Shares shall be delivered to you on the Closing Date or the Option Closing Date, as the case may be, with any transfer taxes payable in connection with the transfer of the Shares to the Underwriter duly paid, against payment of the Purchase Price therefor.

5. Conditions to the Underwriter’s Obligations. The obligations of the Company to sell the Shares to the Underwriter and the obligation of the Underwriter to purchase and pay for the Shares on the Closing Date are subject to the following conditions:

(a) Subsequent to the execution and delivery of this Agreement and prior to the Closing Date:

(i) there shall not have occurred any downgrading, nor shall any notice have been given of any intended or potential downgrading or of any review for a possible change that does not indicate the direction of the possible change, in the rating accorded any of the Company’s securities by any “nationally recognized statistical rating organization,” as such term is defined for purposes of Rule 436(g)(2) under the Securities Act; and

(ii) there shall not have occurred any change, or any development involving a prospective change, in the condition, financial or otherwise, or in the earnings, business or operations of the Company and its subsidiaries, taken as a whole, from that set forth in the Prospectus (exclusive of any amendments or supplements thereto subsequent to the date of this Agreement) that, in your judgment, is material and adverse and that makes it, in your judgment, impracticable to market the Shares on the terms and in the manner contemplated in the Prospectus.

(b) The Underwriter shall have received on the Closing Date a certificate, dated the Closing Date and signed by an executive officer of the Company, to the effect set forth in Section 5(a)(i) above and to the effect that the representations and warranties of the Company contained in this Agreement are true and correct as of the Closing Date and that the Company has complied with all of the agreements and satisfied all of the conditions on its part to be performed or satisfied hereunder on or before the Closing Date.

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The officer signing and delivering such certificate may rely upon the best of his or her knowledge as to proceedings threatened.

(c) The Underwriter shall have received on the Closing Date an opinion of Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C., outside counsel for the Company, dated the Closing Date, to the effect that:

(i) the Company has been duly incorporated, is validly existing as a corporation in good standing under the laws of the jurisdiction of its incorporation, has the corporate power and authority to own its property and to conduct the business in which it is engaged as described in the Prospectus and is in good standing in Utah, the only jurisdiction in which the Company owns real estate or leases property;

(ii) each subsidiary of the Company has been duly incorporated, is validly existing as a corporation in good standing under the laws of the jurisdiction of its incorporation, has the corporate power and authority to own its property and to conduct its business as described in the Prospectus and is duly qualified to transact the business in which it is engaged as described in the Prospectus and is in good standing in Utah, the only jurisdiction in which the Company owns real estate or leases property;

(iii) the authorized capital stock of the Company conforms as to legal matters to the description thereof contained in the Prospectus;

(iv) the shares of Common Stock outstanding prior to the issuance of the Shares have been duly authorized and are validly issued, fully paid and non-assessable;

(v) all of the issued shares of capital stock of each subsidiary of the Company have been duly authorized and validly issued, are fully paid and non-assessable and are owned directly by the Company, free and clear of all liens, encumbrances, equities or claims;

(vi) the Shares have been duly authorized and, when issued and delivered in accordance with the terms of this Agreement, will be validly issued, fully paid and non-assessable, and the issuance of such Shares will not be subject to any preemptive or similar rights;

(vii) this Agreement has been duly authorized, executed and delivered by the Company;

(viii) the execution and delivery by the Company of, and the performance by the Company of its obligations under, this Agreement will not contravene any provision of applicable law or the certificate of incorporation or bylaws of the Company or, to such counsel’s knowledge, any agreement or other instrument binding upon the Company or any of its subsidiaries that is material to the Company and its subsidiaries, taken as a whole, or, to such counsel’s knowledge, any judgment, order or decree of any governmental body, agency or court having jurisdiction over the Company or any subsidiary, and no consent, approval, authorization or order of, or qualification with, any governmental body or agency is required for the performance by the Company of its obligations under this Agreement, except such as may be required by the

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securities or Blue Sky laws of the various states or foreign jurisdictions (with respect to which such counsel expresses no opinions) in connection with the offer and sale of the Shares;

(ix) the statements (A) in the Prospectus under the captions “Description of Common Stock,” “Plan of Distribution,” and “Underwriter” and (B) in the Registration Statement in Item 15, in each case insofar as such statements constitute summaries of the legal matters, documents or proceedings referred to therein, fairly present in all material respects the information called for with respect to such legal matters, documents and proceedings and fairly summarize the matters referred to therein;

(x) to such counsel’s knowledge, there are no legal or governmental proceedings pending or threatened to which the Company or any of its subsidiaries is a party or to which any of the properties of the Company or any of its subsidiaries is subject that are required to be described in the Registration Statement or the Prospectus and are not so described or any statutes, regulations, contracts or other documents that are required to be described in the Registration Statement or the Prospectus or to be filed as exhibits to the Registration Statement that are not described or filed as required;

(xi) the Company is not and, after giving effect to the offering and sale of the Shares and the application of the proceeds thereof as described in the Prospectus, will not be required to register as an “investment company” as such term is defined in the Investment Company Act of 1940, as amended; and

(xii) such counsel (A) is of the opinion that each document, if any, filed pursuant to the Exchange Act and incorporated by reference in the Registration Statement and the Prospectus (except for financial statements and schedules and other financial and statistical data included herein as to which such counsel need not express any opinion) complied when so filed as to form in all material respects with the Exchange Act and the applicable rules and regulations of the Commission thereunder, (B) is of the opinion that the Registration Statement and Prospectus (except for financial statements and schedules and other financial and statistical data derived therefrom as to which such counsel need not express any opinion) comply as to form in all material respects with the Securities Act and the applicable rules and regulations of the Commission thereunder, (C) has no reason to believe that (except for financial statements and schedules and other financial and statistical data derived therefrom as to which such counsel need not express any opinion) the Registration Statement and the Prospectus included therein at the time the Registration Statement became effective contained any untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary to make the statements therein not misleading and (D) has no reason to believe that (except for financial statements and schedules and other financial and statistical data as to which such counsel need not express any belief) the Prospectus contains any untrue statement of a material fact or omits to state a material fact necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading.

(d) The Underwriter shall have received on the Closing Date an opinion of Wilson Sonsini Goodrich & Rosati, Professional Corporation, counsel for the Underwriter, dated the

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Closing Date, covering the matters referred to in Sections 5(c)(vi), 5(c)(vii), 5(c)(ix) (but only as to the statements in the Prospectus under “Description of Common Stock” and “Underwriter,” except as to paragraphs eight and nine of such section) and clauses (B) and (D) of 5(c)(xii) above.

With respect to subparagraph (xii) of paragraph (c) above, Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C. may state that its opinion and belief are based upon its participation in the preparation of the Registration Statement and Prospectus and any amendments or supplements thereto and documents incorporated by reference and review and discussion of the contents thereof, but is without independent check or verification, except as specified. With respect to clauses (B) and (D) of subparagraph (xii) of paragraph (c) above, Wilson Sonsini Goodrich & Rosati, Professional Corporation, may state that its opinion and belief are based upon its participation in the preparation of the Prospectus and any amendments or supplements thereto (other than the documents incorporated by reference) and upon review and discussion of the contents thereof (including documents incorporated by reference), but are without independent check or verification, except as specified.

The opinion of Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C. described in Section 5(c) above shall be rendered to the Underwriter at the request of the Company and shall so state therein.

(e) The Underwriter shall have received a letter dated the Closing Date in form and substance satisfactory to the Underwriter, from KPMG LLP, independent public accountants, containing statements and information of the type ordinarily included in accountants’ “comfort letters” to underwriters with respect to the financial statements and certain financial information contained in, or incorporated by reference into, the Registration Statement and the Prospectus; provided that the letter delivered on the Closing Date shall use a “cut-off date” not earlier than the date hereof.

(f) The “lock-up” agreements, each substantially in the form of Exhibit A hereto, between you and certain shareholders, officers and directors of the Company relating to sales and certain other dispositions of shares of Common Stock or certain other securities, delivered to you on or before the Closing Date.

(g) The Company shall have delivered all other certificates as may be reasonably requested by Wilson Sonsini Goodrich & Rosati, Professional Corporation, counsel to the Underwriter.

The obligation of the Underwriter to purchase Additional Shares hereunder is subject to the delivery to you on the Option Closing Date of such documents as you may reasonably request with respect to the good standing of the Company, the due authorization and issuance of the Additional Shares and other matters related to the issuance of the Additional Shares and an opinion of Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C. in the form of Section 5(c) above, which form shall be deemed to be reasonably satisfactory to Wilson Sonsini Goodrich & Rosati, Professional Corporation, counsel for the Underwriter.

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6. Covenants of the Company. In further consideration of the agreements of the Underwriter herein contained, the Company covenants with the Underwriter as follows:

(a) To furnish you, without charge, two (2) signed copies of the Registration Statement (including exhibits thereto and documents incorporated by reference) and, during the period mentioned in paragraph (c) below, as many copies of the Prospectus, any documents incorporated by reference, and any supplements and amendments thereto as you may reasonably request. The terms “supplement” and “amendment” or “amend” as used in this Agreement shall include all documents subsequently filed by the Company with the Commission pursuant to the Exchange Act that are deemed to be incorporated by reference in the Prospectus.

(b) Before amending or supplementing the Registration Statement or the Prospectus, to furnish to you a copy of each such proposed amendment or supplement and not to file any such proposed amendment or supplement to which you reasonably object, and to file with the Commission within the applicable period specified in Rule 424(b) under the Securities Act any prospectus required to be filed pursuant to such Rule.

(c) If, during such period after the first date of the public offering of the Shares as in the opinion of counsel for the Underwriter the Prospectus is required by law to be delivered in connection with sales by an Underwriter or dealer, any event shall occur or condition exist as a result of which it is necessary to amend or supplement the Prospectus in order to make the statements therein, in the light of the circumstances when the Prospectus is delivered to a purchaser, not misleading, or if, in the opinion of counsel for the Underwriter, it is necessary to amend or supplement the Prospectus to comply with applicable law, forthwith to prepare, file with the Commission and furnish, at its own expense, to the Underwriter and to the dealers (whose names and addresses you will furnish to the Company) to which Shares may have been sold by you on behalf of the Underwriter and to any other dealers upon request, either amendments or supplements to the Prospectus so that the statements in the Prospectus as so amended or supplemented will not, in the light of the circumstances when the Prospectus is delivered to a purchaser, be misleading or so that the Prospectus, as amended or supplemented, will comply with law; provided, however, that in the event that the Underwriter is required to deliver a Prospectus after the nine-month period referred to in Section 10(a)(3) of the Securities Act in connection with the sale of the Shares, the Company will prepare promptly upon request, but at the expense of the Underwriter, such amendment or amendments to the Registration Statement and such Prospectuses as may be necessary to permit compliance with the requirements of Section 10(a)(3) of the Securities Act.

(d) To endeavor to qualify the Shares for offer and sale under the securities or Blue Sky laws of such jurisdictions as you shall reasonably request; provided, however, that the Company shall not be required to qualify as a foreign corporation or to file a general consent to service of process in any jurisdiction.

(e) To make generally available to the Company’s security holders and to you as soon as practicable an earning statement covering the twelve-month period ending June 30, 2005, that satisfies the provisions of Section 11(a) of the Securities Act and the rules and regulations of the Commission thereunder.

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(f) Whether or not the transactions contemplated in this Agreement are consummated or this Agreement is terminated, to pay or cause to be paid all expenses incident to the performance of the Company’s obligations under this Agreement, including: (i) the fees, disbursements and expenses of the Company’s counsel and the Company’s accountants in connection with the registration and delivery of the Shares under the Securities Act and all other fees or expenses in connection with the preparation and filing of the Registration Statement, any preliminary prospectus, the Prospectus and amendments and supplements to any of the foregoing, including all printing costs associated therewith, and the mailing and delivering of copies thereof to the Underwriter and dealers, or other parties designated by the Underwriter, in the quantities hereinabove specified, (ii) all costs and expenses related to the transfer and delivery of the Shares to the Underwriter, including any transfer or other taxes payable thereon, (iii) the cost of printing or producing any Blue Sky or Legal Investment memorandum in connection with the offer and sale of the Shares under state securities laws and all expenses in connection with the qualification of the Shares for offer and sale under state or applicable foreign securities laws as provided in Section 6(d) hereof, including filing fees and the reasonable fees and disbursements of counsel for the Underwriter in connection with such qualification and in connection with the Blue Sky or Legal Investment memorandum, (iv) all filing fees and the reasonable fees and disbursements of counsel to the Underwriter incurred in connection with the review and qualification of the offering of the Shares by the National Association of Securities Dealers, Inc., (v) all costs and expenses incident to listing the Shares on the Nasdaq National Market, (vi) the cost of printing certificates representing the Shares, (vii) the costs and charges of any transfer agent, registrar or depositary, (viii) all other costs and expenses incident to the performance of the obligations of the Company hereunder for which provision is not otherwise made in this Section. It is understood, however, that except as provided in this Section, Section 7 entitled “Indemnity and Contribution,” and the last paragraph of Section 9 below, the Underwriter will pay all of its costs and expenses, including fees and disbursements of its counsel, stock transfer taxes payable on resale of any of the Shares by it and any advertising expenses connected with any offers it may make.

7. Indemnity and Contribution. (a) The Company agrees to indemnify and hold harmless the Underwriter, each person, if any, who controls the Underwriter within the meaning of either Section 15 of the Securities Act or Section 20 of the Exchange Act, and each affiliate of the Underwriter, from and against any and all losses, claims, damages and liabilities (including, without limitation, any legal or other expenses reasonably incurred in connection with defending or investigating any such action or claim) caused by any untrue statement or alleged untrue statement of a material fact contained in the Registration Statement or any amendment thereof, any preliminary prospectus or the Prospectus (as amended or supplemented if the Company shall have furnished any amendments or supplements thereto), or caused by any omission or alleged omission to state therein a material fact required to be stated therein or necessary to make the statements therein not misleading, except insofar as such losses, claims, damages or liabilities are caused by any such untrue statement or omission or alleged untrue statement or omission based upon information relating to the Underwriter furnished to the Company in writing by the Underwriter expressly for use therein.

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(b) The Underwriter agrees, to indemnify and hold harmless the Company, its directors and officers who signed the Registration Statement and each person, if any, who controls the Company within the meaning of either Section 15 of the Securities Act or Section 20 of the Exchange Act to the same extent as the foregoing indemnity from the Company to the Underwriter, but only with reference to information relating to the Underwriter furnished to the Company in writing by the Underwriter expressly for use in the Prospectus or any amendments or supplements thereto.

(c) In case any proceeding (including any governmental investigation) shall be instituted involving any person in respect of which indemnity may be sought pursuant to Section 7(a) or 7(b), such person (the “indemnified party”) shall promptly notify the person against whom such indemnity may be sought (the “indemnifying party”) in writing and the indemnifying party, upon request of the indemnified party, shall retain counsel reasonably satisfactory to the indemnified party to represent the indemnified party and any others the indemnifying party may designate in such proceeding and shall pay the fees and disbursements of such counsel related to such proceeding. In any such proceeding, any indemnified party shall have the right to retain its own counsel, but the fees and expenses of such counsel shall be at the expense of such indemnified party unless (i) the indemnifying party and the indemnified party shall have mutually agreed to the retention of such counsel or (ii) the named parties to any such proceeding (including any impleaded parties) include both the indemnifying party and the indemnified party and representation of both parties by the same counsel would be inappropriate due to actual or potential differing interests between them. It is understood that the indemnifying party shall not, in respect of the legal expenses of any indemnified party in connection with any proceeding or related proceedings in the same jurisdiction, be liable for the fees and expenses of more than one separate firm (in addition to any local counsel) for all such indemnified parties and that all such fees and expenses shall be reimbursed as they are incurred. Such firm shall be designated in writing by Morgan Stanley & Co. Incorporated, in the case of parties indemnified pursuant to Section 7(a), and by the Company, in the case of parties indemnified pursuant to Section 7(b). The indemnifying party shall not be liable for any settlement of any proceeding effected without its written consent, but if settled with such consent or if there be a final judgment for the plaintiff, the indemnifying party agrees to indemnify the indemnified party from and against any loss or liability by reason of such settlement or judgment. Notwithstanding the foregoing sentence, if at any time an indemnified party shall have requested an indemnifying party to reimburse the indemnified party for fees and expenses of counsel as contemplated by the second and third sentences of this paragraph, the indemnifying party agrees that it shall be liable for any settlement of any proceeding effected without its written consent if (i) such settlement is entered into more than 30 days after receipt by such indemnifying party of the aforesaid request and (ii) such indemnifying party shall not have reimbursed the indemnified party in accordance with such request prior to the date of such settlement. No indemnifying party shall, without the prior written consent of the indemnified party, effect any settlement of any pending or threatened proceeding in respect of which any indemnified party is or could have been a party and indemnity could have been sought hereunder by such indemnified party, unless such settlement includes an unconditional release of such indemnified party from all liability on claims that are the subject matter of such proceeding.

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(d) To the extent the indemnification provided for in Section 7(a) or 7(b) is unavailable to an indemnified party or insufficient in respect of any losses, claims, damages or liabilities referred to therein, then each indemnifying party under such paragraph, in lieu of indemnifying such indemnified party thereunder, shall contribute to the amount paid or payable by such indemnified party as a result of such losses, claims, damages or liabilities (i) in such proportion as is appropriate to reflect the relative benefits received by the Company on the one hand and the Underwriter on the other hand from the offering of the Shares or (ii) if the allocation provided by clause 7(d)(i) above is not permitted by applicable law, in such proportion as is appropriate to reflect not only the relative benefits referred to in clause 7(d)(i) above but also the relative fault of the Company on the one hand and of the Underwriter on the other hand in connection with the statements or omissions that resulted in such losses, claims, damages or liabilities, as well as any other relevant equitable considerations. The relative benefits received by the Company on the one hand and the Underwriter on the other hand in connection with the offering of the Shares shall be deemed to be in the same respective proportions as the net proceeds from the offering of the Shares (before deducting expenses) received by the Company and the total underwriting discounts and commissions received by the Underwriter, in each case as set forth in the table on the cover of the Prospectus, bear to the aggregate Public Offering Price of the Shares. The relative fault of the Company on the one hand and the Underwriter on the other hand shall be determined by reference to, among other things, whether the untrue or alleged untrue statement of a material fact or the omission or alleged omission to state a material fact relates to information supplied by the Company or by the Underwriter and the parties’ relative intent, knowledge, access to information and opportunity to correct or prevent such statement or omission.

(e) The Company and the Underwriter agree that it would not be just or equitable if contribution pursuant to this Section 7 were determined by pro rata allocation or by any other method of allocation that does not take account of the equitable considerations referred to in Section 7(d). The amount paid or payable by an indemnified party as a result of the losses, claims, damages and liabilities referred to in the immediately preceding paragraph shall be deemed to include, subject to the limitations set forth above, any legal or other expenses reasonably incurred by such indemnified party in connection with investigating or defending any such action or claim. Notwithstanding the provisions of this Section 7, the Underwriter shall not be required to contribute any amount in excess of the amount by which the total price at which the Shares underwritten by it and distributed to the public were offered to the public exceeds the amount of any damages that the Underwriter has otherwise been required to pay by reason of such untrue or alleged untrue statement or omission or alleged omission. No person guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of the Securities Act) shall be entitled to contribution from any person who was not guilty of such fraudulent misrepresentation. The remedies provided for in this Section 7 are not exclusive and shall not limit any rights or remedies which may otherwise be available to any indemnified party at law or in equity.

(f) The indemnity and contribution provisions contained in this Section 7 and the representations, warranties and other statements of the Company contained in this Agreement shall remain operative and in full force and effect regardless of (i) any termination of this Agreement, (ii) any investigation made by or on behalf of the Underwriter or any person controlling the Underwriter or any affiliate of the Underwriter or by or on behalf of the Company, its officers or directors or any person controlling the Company and (iii) acceptance of and payment for any of the Shares.

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8. Termination. The Underwriter may terminate this Agreement by notice given by you to the Company, if after the execution and delivery of this Agreement and prior to the Closing Date (i) trading generally shall have been suspended or materially limited on or by, as the case may be, any of the New York Stock Exchange, the American Stock Exchange, the Nasdaq National Market, the Chicago Board of Options Exchange, the Chicago Mercantile Exchange or the Chicago Board of Trade, (ii) trading of any securities of the Company shall have been suspended on any exchange or in any over-the-counter market, (iii) a material disruption in securities settlement, payment or clearance services in the United States shall have occurred, (iv) a general moratorium on commercial banking activities in New York shall have been declared by either Federal or New York State authorities or (v) there shall have occurred any outbreak or escalation of hostilities or any change in financial markets or any calamity, crisis or terrorist act that, in your judgment, is material and adverse which, singly or together with any other such event, makes it, in your judgment, impracticable or inadvisable to proceed with the offer, sale or delivery of the Shares on the terms and in the manner contemplated in the Prospectus.

9. Effectiveness. This Agreement shall become effective upon the execution and delivery hereof by the parties hereto.

If this Agreement shall be terminated by the Underwriter, because of any failure or refusal on the part of the Company to comply with the terms or to fulfill any of the conditions of this Agreement, or if for any reason the Company shall be unable to perform its obligations under this Agreement, the Company will reimburse the Underwriter for all out-of-pocket expenses (including the fees and disbursements of its counsel) reasonably incurred by the Underwriter in connection with this Agreement or the offering contemplated hereunder.

10. Counterparts. This Agreement may be signed in two or more counterparts, each of which shall be an original, with the same effect as if the signatures thereto and hereto were upon the same instrument.

11. Applicable Law. This Agreement shall be governed by and construed in accordance with the internal laws of the State of New York.

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12. Headings. The headings of the sections of this Agreement have been inserted for convenience of reference only and shall not be deemed a part of this Agreement.

Exhibit A

Myriad Genetics, Inc.

Lock-up Letter

June [    ], 2004

Morgan Stanley & Co. Incorporated

1585 Broadway

New York, NY 10036

Dear Sirs and Mesdames:

The undersigned understands that Morgan Stanley & Co. Incorporated (the “Underwriter”) proposes to enter into an Underwriting Agreement (the “Underwriting Agreement”) with Myriad Genetics, Inc., a Delaware corporation (the “Company”) providing for the public offering (the “Public Offering”) by the Underwriter of that number of shares the Company agrees to sell and the Underwriter agrees to buy, as set forth in the Underwriting Agreement (the “Shares”), of the Common Stock, $0.01 par value, of the Company (the “Common Stock”).

To induce the Underwriter to continue its efforts in connection with the Public Offering, the undersigned hereby agrees that, without the prior written consent of the Underwriter, it will not, during the period commencing on the date hereof and ending 90 days after the date of the final prospectus supplement relating to the Public Offering (the “Prospectus Supplement”), (1) offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, lend, or otherwise transfer or dispose of, directly or indirectly, any shares of Common Stock or any securities convertible into or exercisable or exchangeable for Common Stock or (2) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of Common Stock, whether any such transaction described in clause (1) or (2) above is to be settled by delivery of Common Stock or such other securities, in cash or otherwise. The foregoing sentence shall not apply to (a) transactions relating to shares of Common Stock or other securities acquired in open market transactions after the completion of the Public Offering, (b) sales by officers and directors at the Company pursuant to plans established in accordance with Rule 10b5-1 under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), (c) transfers of shares of Common Stock or any security convertible into Common Stock as a bona fide gift or gifts, and (d) transfers of shares of Common Stock or any security convertible into Common Stock by the undersigned to its affiliates, as such term is defined in Rule 405 under the Securities Act of 1933, as amended; provided that in the case of any transfer or distribution pursuant to clause (c) or (d), (i) each donee or distributee shall execute and deliver to Morgan Stanley a duplicate form of this Lock-up Letter and (ii) no filing by any party (donor, donee, transferor or transferee) under Section 16(a) of the Exchange Act shall be required or shall be made voluntarily in connection with such transfer or distribution (other than a filing on a Form 5 made after the expiration of the 90-day period referred to above).

In addition, the undersigned agrees that, without the prior written consent of the Underwriter, it will not, during the period commencing on the date hereof and ending 90 days after the date of the Prospectus Supplement, make any demand for or exercise any right with respect to, the registration of any shares of Common Stock or any security convertible into or exercisable or exchangeable for Common Stock. The undersigned also agrees and consents to the entry of stop transfer instructions with the Company’s transfer agent and registrar against the transfer of the undersigned’s shares of Common Stock except in compliance with the foregoing restrictions.

The undersigned understands that the Company and the Underwriter are relying upon this Lock-Up Agreement in proceeding toward consummation of the Public Offering. The undersigned further understands that this Lock-Up Agreement is irrevocable and shall be binding upon the undersigned’s heirs, legal representatives, successors and assigns.

Whether or not the Public Offering actually occurs depends on a number of factors, including market conditions. Any Public Offering will only be made pursuant to an Underwriting Agreement, the terms of which are subject to negotiation between the Company and the Underwriter.

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