<PAGE>

THIS WARRANT AND THE SHARES ISSUABLE HEREUNDER HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE SOLD, PLEDGED, OR
OTHERWISE TRANSFERRED WITHOUT AN EFFECTIVE REGISTRATION THEREOF UNDER SUCH ACT
OR PURSUANT TO RULE 144 OR AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE
CORPORATION AND ITS COUNSEL, THAT SUCH REGISTRATION IS NOT REQUIRED.


                           WARRANT TO PURCHASE STOCK

Corporation:  Durect Corporation, a Delaware corporation
Number of Shares:  31,395
Class of Stock:  Series B-1 Preferred
Initial Exercise Price: $2.15
Issue Date: December 16, 1999
Expiration Date: December 16, 2006


     THIS WARRANT CERTIFIES THAT, for the agreed upon value of $1.00 and for
other good and valuable consideration, SILICON VALLEY BANK ("Holder") is
entitled to purchase the number of fully paid and nonassessable shares of the
class of securities (the "Shares") of the corporation (the "Company") at the
initial exercise price per Share (the "Warrant Price") all as set forth above
and as adjusted pursuant to Article 2 of this Warrant, subject to the provisions
and upon the terms and conditions set forth in this Warrant.

ARTICLE 1. EXERCISE.
           --------

           1.1  Method of Exercise.  Holder may exercise this Warrant by
                ------------------
delivering a duly executed Notice of Exercise in substantially the form attached
as Appendix 1 to the principal office of the Company.  Unless Holder is
exercising the conversion right set forth in Section 1.2, Holder shall also
deliver to the Company a check for the aggregate Warrant Price for the Shares
being purchased.

           1.2  Conversion Right.  In lieu of exercising this Warrant as
                ----------------
specified in Section 1.1, Holder may from time to time convert this Warrant, in
whole or in part, into a number of Shares determined by dividing (a) the
aggregate fair market value of the Shares or other securities otherwise issuable
upon exercise of this Warrant minus the aggregate Warrant Price of such Shares
by (b) the fair market value of one Share.  The fair market value of the Shares
shall be determined pursuant to Section 1.4.

           1.3  Intentionally Omitted
                ---------------------

           1.4  Fair Market Value.  If the Shares are traded in a public market,
                -----------------
the fair market value of the Shares shall be the closing price of the Shares (or
the closing price of the Company's stock into which the Shares are convertible)
reported for the business day immediately before Holder delivers its Notice of
Exercise to the Company.  If the Shares are not traded in a public market, the
Board of Directors of the Company shall determine fair market value in its
reasonable good faith judgment.

           1.5  Delivery of Certificate and New Warrant.  Promptly after Holder
                ---------------------------------------
exercises or converts this Warrant, the Company shall deliver to Holder
certificates for the Shares acquired and, if this Warrant has not been fully
exercised or converted and has not expired, a new Warrant representing the
Shares not so acquired.

           1.6  Replacement of Warrants.  On receipt of evidence reasonably
                -----------------------
satisfactory to the Company of the loss, theft, destruction or mutilation of
this Warrant and, in the case of loss, theft or destruction, on delivery of an
indemnity agreement reasonably satisfactory in form and amount to the Company
or, in the case of mutilation, on surrender and cancellation of this Warrant,
the Company at its expense shall execute and deliver, in lieu of this Warrant, a
new warrant of like tenor.
<PAGE>

           1.7  Repurchase on Sale, Merger, or Consolidation of the Company.
                -----------------------------------------------------------

                1.7.1.    "Acquisition".  For the purpose of this Warrant,
                          -------------
"Acquisition" means any sale, license, or other disposition of all or
substantially all of the assets of the Company, or any reorganization,
consolidation, or merger of the Company where the holders of the Company's
securities before the transaction beneficially own less than 50% of the
outstanding voting securities of the surviving entity after the transaction.

                1.7.2.    Assumption of Warrant. If upon the closing of any
                          ---------------------
Acquisition Holder has not otherwise exercised this Warrant in full, then the
unexercised portion of this Warrant shall be deemed to have been automatically
converted pursuant to Section 1.2 and thereafter, Holder shall participate in
the acquisition on the same terms as other holders of the same class of
securities of the Company.

         1.8  Exercise upon IPO.  With respect to an underwritten initial public
              -----------------
offering of the Shares of the Company where the net proceeds to the Company are
in excess of at least $10,000,000, the Warrant shall be deemed automatically
exercised on a net exercise basis on the first date the Bank is permitted to
sell the Shares without restriction.

ARTICLE 2. ADJUSTMENTS TO THE SHARES.
           -------------------------

           2.1  Stock Dividends, Splits, Etc.   If the Company declares or
                ----------------------------
pays a dividend on its common stock (or the Shares if the Shares are securities
other than common stock) payable in common stock, or other securities,
subdivides the outstanding common stock into a greater amount of common stock,
or, if the Shares are securities other than common stock, subdivides the Shares
in a transaction that increases the amount of common stock into which the Shares
are convertible, then upon exercise of this Warrant, for each Share acquired,
Holder shall receive, without cost to Holder, the total number and kind of
securities to which Holder would have been entitled had Holder owned the Shares
of record as of the date the dividend or subdivision occurred.

           2.2  Reclassification, Exchange or Substitution.  Upon any
                ------------------------------------------
reclassification, exchange, substitution, or other event that results in a
change of the number and/or class of the securities issuable upon exercise or
conversion of this Warrant, Holder shall be entitled to receive, upon exercise
or conversion of this Warrant, the number and kind of securities and property
that Holder would have received for the Shares if this Warrant had been
exercised immediately before such reclassification, exchange, substitution, or
other event.  Such an event shall include any automatic conversion of the
outstanding or issuable securities of the Company of the same class or series as
the Shares to common stock pursuant to the terms of the Company's Articles of
Incorporation upon the closing of a registered public offering of the Company's
common stock.  The Company or its successor shall promptly issue to Holder a new
Warrant for such new securities or other property.  The new Warrant shall
provide for adjustments which shall be as nearly equivalent as may be
practicable to the adjustments provided for in this Article 2 including, without
limitation, adjustments to the Warrant Price and to the number of securities or
property issuable upon exercise of the new Warrant.  The provisions of this
Section 2.2 shall similarly apply to successive reclassifications, exchanges,
substitutions, or other events.

           2.3  Adjustments for Combinations, Etc.  If the outstanding shares
                ---------------------------------
are combined or consolidated, by reclassification or otherwise, into a lesser
number of shares, the Warrant Price shall be proportionately increased.

           2.4  Adjustments for Diluting Issuances.  The Warrant Price and the
                ----------------------------------
number of Shares issuable upon exercise of this Warrant or, if the Shares are
Preferred Stock, the number of shares of common stock issuable upon conversion
of the Shares, shall be subject to adjustment, from time to time in the manner
set forth on Exhibit A in the event of Diluting Issuances (as defined on Exhibit
A).
<PAGE>

           2.5  No Impairment.  The Company shall not, by amendment of its
                -------------
Articles of Incorporation or through a 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 under this Warrant by the Company, but
shall at all times in good faith assist in carrying out of all the provisions of
this Article 2 and in taking all such action as may be necessary or appropriate
to protect Holder's rights under this Article against impairment.  If the
Company takes any action affecting the Shares or its common stock other than as
described above that adversely affects Holder's rights under this Warrant, the
Warrant Price shall be adjusted downward and the number of Shares issuable upon
exercise of this Warrant shall be adjusted upward in such a manner that the
aggregate Warrant Price of this Warrant is unchanged.

           2.6  Fractional Shares.  No fractional Shares shall be issuable upon
                -----------------
exercise or conversion of the Warrant and the number of Shares to be issued
shall be rounded down to the nearest whole Share.  If a fractional share
interest arises upon any exercise or conversion of the Warrant, the Company
shall eliminate such fractional share interest by paying Holder an amount
computed by multiplying the fractional interest by the fair market value of a
full Share.

           2.7  Certificate as to Adjustments.  Upon each adjustment of the
                -----------------------------
Warrant Price, the Company at its expense shall promptly compute such
adjustment, and furnish Holder with a certificate of its Chief Financial Officer
setting forth such adjustment and the facts upon which such adjustment is based.
The Company shall, upon written request, furnish Holder a certificate setting
forth the Warrant Price in effect upon the date thereof and the series of
adjustments leading to such Warrant Price.

ARTICLE 3. REPRESENTATIONS AND COVENANTS OF THE COMPANY.
           --------------------------------------------

           3.1  Representations and Warranties.  The Company hereby represents
                ------------------------------
and warrants to the Holder as follows:

                (a) The initial Warrant Price referenced on the first page of
this Warrant is not greater than (i) the price per share at which shares of the
Company's Series B Preferred Stock were last issued in an arms-length
transaction in which at least $500,000 of such Series B Preferred Stock was
sold.

                (b) All Shares which may be issued upon the exercise of the
purchase right represented by this Warrant, and all securities, if any, issuable
upon conversion of the Shares, shall, upon issuance, be duly authorized, validly
issued, fully paid and nonassessable, and free of any liens and encumbrances
except for restrictions on transfer provided for herein or under applicable
federal and state securities laws.

                (c) The Capitalization Table attached to this Warrant is true
and complete as of the Issue Date.

           3.2  Notice of Certain Events.  If the Company proposes at any time
                ------------------------
(a) to declare any dividend or distribution upon its common stock, whether in
cash, property, stock, or other securities and whether or not a regular cash
dividend; (b) to effect any reclassification or recapitalization of common
stock; (c) to merge or consolidate with or into any other corporation, or sell,
lease, license, or convey all or substantially all of its assets, or to
liquidate, dissolve or wind up; or (d) offer holders of registration rights the
opportunity to participate in an underwritten public offering of the company's
securities for cash, then, in connection with each such event, the Company shall
give Holder (1) at least 10 days prior written notice of the date on which a
record will be taken for such dividend, distribution, or subscription rights
(and specifying the date on which the holders of common stock will be entitled
thereto) or for determining rights to vote, if any, in respect of the matters
referred to in (b) and (c) above; (2) in the case of the matters referred to in
(b) and (c) above at least 10 days prior written notice of the date when the
same will take place (and specifying the date on which the holders of common
stock will be entitled to exchange their common stock for securities or other
property deliverable upon the occurrence of such event); and (3) in the case of
the matter referred to in (d) above, the same notice as is given to the holders
of such registration rights.
<PAGE>

           3.3  Information Rights.  So long as the Holder holds this Warrant
                ------------------
and/or any of the Shares, the Company shall deliver to the Holder (a) promptly
after mailing, copies of all notices or other written communications to the
shareholders of the Company, (b) within ninety (90) days after the end of each
fiscal year of the Company, the annual audited financial statements of the
Company certified by independent public accountants of recognized standing and
(c) such other financial statements required under and in accordance with any
loan documents between Holder and the Company (or if there are no such
requirements [or if the subject loan(s) no longer are outstanding]), then within
forty-five (45) days after the end of each of the first three quarters of each
fiscal year, the Company's quarterly, unaudited financial statements.

           3.4  Registration Under Securities Act of 1933, as amended.  The
                -----------------------------------------------------
Company agrees that the Shares or, if the Shares are convertible into common
stock of the Company, such common stock, shall be subject to the registration
rights set forth in the Company's Investors' Rights Agreement.

ARTICLE 4. MISCELLANEOUS.
           -------------

           4.1  Term.  This Warrant is exercisable, in whole or in part, at any
                ----
time and from time to time on or before the Expiration Date set forth above
except as set forth in Section 1.7.2.  The Company shall give Holder written
notice of Holder's right to exercise this Warrant in the form attached as
Appendix 2 not more than 90 days and not less than 30 days before the Expiration
Date. If the notice is not so given, the Expiration Date shall automatically be
extended until 30 days after the date the Company delivers the notice to Holder.

           4.2  Legends.  This Warrant and the Shares (and the securities
                -------
issuable, directly or indirectly, upon conversion of the Shares, if any) shall
be imprinted with a legend in substantially the following form:

     THIS SECURITY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS
     AMENDED, AND MAY NOT BE SOLD, PLEDGED OR OTHERWISE TRANSFERRED WITHOUT AN
     EFFECTIVE REGISTRATION THEREOF UNDER SUCH ACT OR PURSUANT TO RULE 144 OR AN
     OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE CORPORATION AND ITS
     COUNSEL THAT SUCH REGISTRATION IS NOT REQUIRED.

           4.3  Compliance with Securities Laws on Transfer.  This Warrant and
                -------------------------------------------
the Shares issuable upon exercise this Warrant (and the securities issuable,
directly or indirectly, upon conversion of the Shares, if any) may not be
transferred or assigned in whole or in part without compliance with applicable
federal and state securities laws by the transferor and the transferee
(including, without limitation, the delivery of investment representation
letters and legal opinions reasonably satisfactory to the Company, as reasonably
requested by the Company).  The Company shall not require Holder to provide an
opinion of counsel if the transfer is to an affiliate of Holder or if there is
no material question as to the availability of current information as referenced
in Rule 144(c), Holder represents that it has complied with Rule 144(d) and (e)
in reasonable detail, the selling broker represents that it has complied with
Rule 144(f), and the Company is provided with a copy of Holder s notice of
proposed sale.

           4.4  Transfer Procedure.  Subject to the provisions of Section 4.3
                ------------------
Holder may transfer all or part of this Warrant or the Shares issuable upon
exercise of this Warrant (or the securities issuable, directly or indirectly,
upon conversion of the Shares, if any) at any time to Silicon Valley Bancshares
or The Silicon Valley Bank Foundation, or to any affiliate of Holder, or, to any
other transferree by giving the Company notice of the portion of the Warrant
being transferred setting forth the name, address and taxpayer identification
number of the transferee and surrendering this Warrant to the Company for
reissuance to the transferee(s) (and Holder if applicable).  Unless the Company
is filing financial information with the SEC pursuant to the Securities Exchange
Act of 1934, the Company shall have the right to refuse to transfer any portion
of this Warrant to any person who directly competes with the Company.

           4.5  Notices.  All notices and other communications from the Company
                -------
to the Holder, or vice versa, shall be deemed delivered and effective when given
personally or mailed by first-class registered or certified mail at such address
as may have been furnished to the Company or the Holder, as
<PAGE>

the case may be, in writing by the Company or such holder from time to time. All
notices to be provided under this Warrant shall be sent to the following
address:

                Silicon Valley Bank
                Attn: Treasury Department
                3003 Tasman Drive
                Santa Clara, CA  95054


           4.6  Waiver.  This Warrant and any term hereof may be changed,
                ------
waived, discharged or terminated only by an instrument in writing signed by the
party against which enforcement of such change, waiver, discharge or termination
is sought.

           4.7  Attorneys Fees.  In the event of any dispute between the parties
                --------------
concerning the terms and provisions of this Warrant, the party prevailing in
such dispute shall be entitled to collect from the other party all costs
incurred in such dispute, including reasonable attorneys' fees.

           4.8  Governing Law.  This Warrant shall be governed by and construed
                -------------
in accordance with the laws of the State of California, without giving effect to
its principles regarding conflicts of law.


                                    "COMPANY"

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


                                    By:    /s/ James E. Brown
                                           ---------------------------

                                    Name:  President
                                           ---------------------------
                                           (Print)
                                    Title: Chairman of the Board, President or
                                           Vice President


                                    By:    /s/ Thomas A. Schreck
                                           ---------------------------

                                    Name:  Chief Financial Officer
                                           ---------------------------
                                           (Print)
                                    Title: Chief Financial Officer, Secretary,
                                           Assistant Treasurer or Assistant
                                           Secretary
<PAGE>

                                   APPENDIX 1


                               NOTICE OF EXERCISE
                               ------------------



     1.   The undersigned hereby elects to purchase _____________ shares of the
Common/Preferred Series ___ [Strike one] Stock of ______________. pursuant to
the terms of the attached Warrant, and tenders herewith payment of the purchase
price of such shares in full.

     2.   The undersigned hereby elects to convert the attached Warrant into
Shares/cash [strike one] in the manner specified in the Warrant.  This
conversion is exercised with respect to _____________________ of the Shares
covered by the Warrant.

     [Strike paragraph that does not apply.]

     3.   Please issue a certificate or certificates representing said shares in
the name of the undersigned or in such other name as is specified below:

               ___________________________________________
                    (Name)


               ___________________________________________

               ___________________________________________
                    (Address)

     4.   The undersigned represents it is acquiring the shares solely for its
own account and not as a nominee for any other party and not with a view toward
the resale or distribution thereof except in compliance with applicable
securities laws.

                                    ____________________________________
                                         (Signature)

____________________
     (Date)
<PAGE>

                                  APPENDIX 2

                    Notice that Warrant Is About to Expire
                    --------------------------------------

                          _____________________, ___


(Name of Holder)

(Address of Holder)

Attn: Chief Financial Officer


Dear : ______________________

     This is to advise you that the Warrant issued to you described below will
expire on  _________________________, 19___.

     Issuer:

     Issue Date:

     Class of Security Issuable:

     Exercise Price per Share:

     Number of Shares Issuable:

     Procedure for Exercise:

     Please contact [name of contact person at (phone number)] with any
questions you may have concerning exercise of the Warrant. This is your only
notice of pending expiration.


                                        -------------------------------------
                                        (Name of Issuer)

                                        By:
                                            ---------------------------------

                                        Its:
                                            ---------------------------------
<PAGE>

                                   EXHIBIT A
                                   ---------

                            Anti-Dilution Provisions
     (For Preferred Stock Warrants With Existing Anti-Dilution Protection)
      -------------------------------------------------------------------


     In the event of the issuance (a "Diluting Issuance") by the Company, after
the Issue Date of the Warrant, of securities at a price per share less than the
Warrant Price, then the number of shares of common stock issuable upon
conversion of the Shares shall be adjusted in accordance with those provisions
(the "Provisions") of the Company's Certificate of Designation of Rights,
Preferences and Privileges which apply to Diluting Issuances.

     The Company agrees that the Provisions, as in effect on the Issue Date,
shall be deemed to remain in full force and effect during the term of the
Warrant notwithstanding any subsequent amendment, waiver or termination thereof
by the Company's shareholders.

     Under no circumstances shall the aggregate Warrant Price payable by the
Holder upon exercise of the Warrant increase as a result of any adjustment
arising from a Diluting Issuance.