<PAGE>

                                                                     Exhibit 4.3
                                                                  Execution Copy

THE SECURITIES REPRESENTED BY THIS WARRANT CERTIFICATE AND THE SHARES OF STOCK
ISSUABLE UPON EXERCISE HEREOF HAVE BEEN ACQUIRED FOR INVESTMENT AND HAVE NOT
BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"), OR ANY
                                                                   ---
SECURITIES LAWS OF A STATE OR OTHER JURISDICTION AND MAY NOT UNDER ANY
CIRCUMSTANCES BE SOLD, TRANSFERRED OR OTHERWISE DISPOSED OF (OTHER THAN TO AN
AFFILIATE OR AS OTHERWISE PERMITTED BY THIS WARRANT CERTIFICATE PURSUANT TO
WHICH THEY WERE ISSUED) EXCEPT PURSUANT TO (i) AN EFFECTIVE REGISTRATION
STATEMENT UNDER THE ACT AND ANY APPLICABLE STATE SECURITIES OR BLUE SKY LAWS, OR
(ii) TO THE EXTENT APPLICABLE, RULE 144 UNDER THE ACT (OR ANY SIMILAR RULE UNDER
THE ACT RELATING TO THE DISPOSITION OF SECURITIES) TOGETHER WITH AN OPINION OF
COUNSEL SATISFACTORY TO INCARA PHARMACEUTICALS CORPORATION THAT REGISTRATION IS
NOT REQUIRED UNDER THE ACT OR APPLICABLE STATE SECURITIES LAWS.

                      INCARA PHARMACEUTICALS CORPORATION

                          WARRANT TO PURCHASE SHARES
                          OF SERIES B PREFERRED STOCK

          THIS CERTIFIES THAT, for value received, Elan International Services,
Ltd., a Bermuda exempted limited liability company, or its permitted transferees
and successors as provided herein (each, a "Holder"), is entitled to subscribe
                                            ------
for and purchase up to 22,191 shares, as adjusted pursuant to Section 4 (the
"Shares"), of the fully paid and nonassessable Series B Convertible Preferred
 ------
Stock, par value U.S.$0.01 per share (the "Series B Preferred Stock"), of Incara
                                           ------------------------
Pharmaceuticals Corporation, a Delaware corporation (the "Company"), at the
                                                          -------
price of U.S.$72.12 per share (such price, and such other prices that shall
result from time to time, from the adjustments specified in Section 4, the
"Warrant Price"), subject to the provisions and upon the terms and conditions
 -------------
hereinafter set forth.

          1.   Term. Subject to the limitations set forth in Sections 3 and 4,
               ----
the purchase right represented by this Warrant is exercisable, in whole or in
part, at any time, and from time to time, from and after the date hereof and
until 5:00 p.m. Eastern Standard Time, December 21, 2005.  To the extent not
exercised at 5:00 p.m. Eastern Standard Time on December 21, 2005, this Warrant
shall completely and automatically terminate and expire, and thereafter it shall
be of no force or effect.
<PAGE>

          2.   Method of Exercise; Payment; Issuance of New Warrant. (a) The
               ----------------------------------------------------
purchase right represented by this Warrant may be exercised by the Holder, in
whole or in part and from time to time, by the surrender of this Warrant (with
the notice of exercise form attached hereto as Annex A duly executed) at the
                                               -------
principal office of the Company and by the payment to the Company of an amount,
at the option of the Holder, (i) in cash or other immediately available funds,
(ii) by the surrender of this Warrant (or a portion hereof) in accordance with
the terms hereof but without payment in cash (a "Cashless Exercise") or (iii)
                                                 -----------------
with any combination of (i) and (ii). The number of shares of Series B Preferred
Stock issuable in respect of a Cashless Exercise shall be computed using the
following formula:

                    X = Y (A-B)
                        -------
                           A

     Where:                        X =  the number of shares of Series B
                              Preferred Stock to be issued to the Holder in
                              respect of a Cashless Exercise

                                   Y =  the number of shares of Series B
                              Preferred Stock purchasable under the Warrant or,
                              if only a portion of the Warrant is being
                              exercised, the portion of the Warrant being
                              canceled in connection with such Cashless Exercise
                              (at the date of such calculation)

                                   A =  the Fair Market Value (as defined below)
                              of one share of the Company's Series B Preferred
                              Stock (at the date of such calculation)

                                   B =  Warrant Price (as adjusted to the date
                              of such calculation)

          The "Fair Market Value" of one share of Series B Preferred Stock shall
               -----------------
be equal to 10 times the closing sale price for the Company's common stock the
day prior to exercise, adjusted appropriately to reflect the then-current
conversion ratio of the Series B Preferred Stock pursuant to the Certificate of
Incorporation of the Company (which conversion ratio is equal to 10 shares of
common stock of the Company for each share of Series B Preferred Stock on the
date hereof); provided, however, that if the Company's common stock is no longer
traded on a securities exchange, the Nasdaq National Market or the Nasdaq
SmallCap Market the Fair Market Value shall be determined  by the Company's
Board of Directors in good faith and reasonably agreed to by the holders of the
Series B Preferred Stock.

          (b)  The persons or entities in whose name(s) any certificate(s)
representing Shares shall be issuable upon exercise of this Warrant shall be
deemed to have become the holder(s) of record of, and shall be treated for all
purposes as the record holder(s) of, the Shares represented thereby (and such
Shares shall be deemed to have been issued) immediately prior to the close of
business on the date or dates upon which this Warrant is properly exercised and
full payment for the Shares acquired pursuant to such exercise is made. Upon any
exercise of the rights represented by this Warrant, certificates for the Shares
purchased

                                       2
<PAGE>

shall be delivered to the holder hereof as soon as possible and in any event
within 30 days of receipt of such notice and payment, and unless this Warrant
has been fully exercised or expired, a new Warrant representing the portion of
Shares, if any, with respect to which this Warrant shall not then have been
exercised shall also be issued to the holder hereof as soon as possible and in
any event within such 30-day period.

          3.   Stock Fully Paid, Reservation of Shares. All Shares that may be
               ---------------------------------------
issued upon the exercise of this Warrant will, upon issuance, be duly and
validly authorized and issued, fully paid and nonassessable, and will be free
from all transfer taxes, liens and charges with respect to the issue thereof and
assuming payment of the Warrant Price for all Shares so purchased, legally and
validly owned by the Holder. During the period within which this Warrant may be
exercised, the Company will at all times have authorized, and reserved for the
purpose of the issue upon the exercise of the purchase rights evidenced by this
Warrant, a sufficient number of shares of Series B Preferred Stock to provide
for the exercise of the rights represented by this Warrant.

          4.   Adjustment of Warrant Price and Number of Shares. The number and
               ------------------------------------------------
kind of securities purchasable upon the exercise of this Warrant and the Warrant
Price shall be subject to the adjustment from time to time upon the occurrence
of certain events, as follows:

          (a)  Reclassification, Etc.  In case of (i) any reclassification,
               ---------------------
reorganization, change or conversion of securities of the class issuable upon
exercise of this Warrant (other than a change in par value, or from par value to
no par value) into other shares or securities of the Company, or (ii) any
consolidation of the Company with or into another entity (other than a merger or
consolidation with another entity in which the Company is the acquiring and the
surviving entity and that does not result in any reclassification or change of
outstanding securities issuable upon exercise of this Warrant), or (iii) any
sale of all or substantially all the assets of the Company, then the Company, or
such successor or purchasing entity, as the case may be, shall duly execute and
deliver to the holder of this Warrant a new Warrant or a supplement hereto (in
form and substance reasonably satisfactory to the holder of this Warrant), so
that the Holder shall have the right to receive, at a total purchase price not
to exceed that payable upon the exercise of the unexercised portion of this
Warrant, and in lieu of the shares of Series B Preferred Stock theretofore
issuable upon the exercise of this Warrant, the kind and amount of shares of
stock and other securities, receivable upon such reclassification,
reorganization, change or conversion by a holder of the number of shares of
Series B Preferred Stock then purchasable under this Warrant. Such new Warrant
shall provide for adjustments that shall be as nearly equivalent as may be
practicable to the adjustments provided for in this Section 4. The provisions of
this Section 4(a) shall similarly attach to successive reclassifications,
reorganizations, changes, and conversions.

          (b)  Splits; Subdivisions. (i) If at any time prior to the earlier of
               --------------------
     the exercise or expiration hereof the Company shall fix a record date for
     the effectuation of a split or subdivision of the outstanding shares of
     Series B Preferred Stock or the determination of holders of Series B
     Preferred Stock entitled to receive a dividend or other distribution
     payable in additional shares of Series B Preferred Stock or other
     securities or property or rights convertible into, or entitling the holder
     thereof to receive directly

                                       3
<PAGE>

     or indirectly, any of the foregoing (hereinafter referred to as "Series B
                                                                      --------
     Stock Equivalents") without payment of any consideration by such holder for
     -----------------
     the additional shares of Series B Preferred Stock or the Series B Preferred
     Stock Equivalents (including the additional shares of Series B Preferred
     Stock issuable upon conversion or exercise thereof) then, this Warrant
     shall be adjusted for, in addition to the number of shares of the Series B
     Preferred Stock otherwise deliverable upon exercise of this Warrant, and
     without adjustment to the Warrant Price, the amount of such additional
     shares of Series B Preferred Stock and any Series B Preferred Stock
     Equivalents that the holder hereof would have received or become entitled
     to receive on the same terms and conditions as if such holder had been a
     holder of record of such Series B Preferred Stock as shall have been
     deliverable immediately prior to such record date pursuant to the terms of
     this Section 4; or

          (ii) If the Company at any time during which this Warrant remains
     outstanding and unexpired shall subdivide or combine its Series B Preferred
     Stock, (A) in the case of a subdivision, the Warrant Price shall be
     proportionately decreased and the number of Shares purchasable hereunder
     shall be proportionately increased, and (B) in the case of a combination,
     the Warrant Price shall be proportionately increased and the number of
     Shares purchasable hereunder shall be proportionately decreased.

               (iii) The following provisions shall apply for purposes of this
     Section 4:

               (A)   the aggregate maximum number of shares of Series B
          Preferred Stock or other securities or property deliverable upon
          conversion or exercise of Series B Preferred Stock Equivalents
          (assuming the satisfaction of any conditions to convertibility or
          exercisability, including, without limitation, the passage of time,
          but without taking into account potential antidilution adjustments)
          shall be deemed to have been issued at the time such Series B
          Preferred Stock Equivalents were issued;

               (B)  in the event of any change in the number of shares of Series
          B Preferred Stock deliverable or in the consideration payable to the
          Company upon conversion or exercise of such Series B Preferred Stock
          Equivalents including, but not limited to, a change resulting from the
          antidilution provisions thereof, the Warrant Price, to the extent in
          any way affected by or computed using such Series B Preferred Stock
          Equivalents, shall be recomputed to reflect such change, but no
          further adjustment shall be made for the actual issuance of Series B
          Preferred Stock or any payment of such consideration upon the exercise
          of any such options or rights or the conversion or exchange of such
          securities; and

               (C)  upon the termination or expiration of the convertibility or
          exercisability of any such Series B Preferred Stock Equivalents, the
          Warrant Price, to the extent in any way affected by or computed using
          such Series B Preferred Stock Equivalents, shall be recomputed to
          reflect the issuance of only the

                                       4
<PAGE>

          number of shares of Series B Preferred Stock (and Series B Preferred
          Stock Equivalents which remain convertible or exercisable) actually
          issued upon the conversion or exercise of such Series B Preferred
          Stock Equivalents.

          (c)  No Impairment. The Company will not, by amendment of its
               -------------
Certificate of Incorporation or bylaws or through any reorganization,
recapitalization, 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
hereunder by the Company, but will at all times in good faith assist in the
carrying out of all the provisions of this Section 4 and in the taking of all
such action as may be necessary or appropriate in order to protect the rights of
the Holder against impairment.

          (d)  Notice of Adjustments. Whenever the Warrant Price or the number
               ---------------------
of Shares purchasable hereunder shall be adjusted pursuant to this Section 4,
the Company shall prepare a certificate setting forth, in reasonable detail, the
event requiring the adjustment, the amount of the adjustment, the method by
which such adjustment was calculated.  Such certificate shall be signed by its
chief financial officer and shall be delivered to the Holder.

          (e)  Fractional Shares. No fractional shares of Series B Preferred
               -----------------
Stock will be issued in connection with any exercise hereunder, but in lieu of
such fractional shares the Company shall make a cash payment therefor based on
the fair market value of the Series B Preferred Stock on the date of exercise as
reasonably determined in good faith by the Company's Board of Directors.

          (f)  Cumulative Adjustments. No adjustment in the Warrant Price shall
               ----------------------
be required under this Section 4 until cumulative adjustments result in a
concomitant change of 1% or more of the Warrant Price or in the number of shares
of Series B Preferred Stock purchasable upon exercise of this Warrant as in
effect prior to the last such adjustment; provided, however, that any adjustment
                                          --------  -------
that by reason of this Section 4 are not required to be made shall be carried
forward and taken into account in any subsequent adjustment.  All calculations
under this Section 4 shall be made to the nearest cent or to the nearest one-
hundredth of a share, as the case may be.

          5.   Compliance with Securities Act; Disposition of Warrant or Shares
               ----------------------------------------------------------------
of Series B Preferred Stock.
---------------------------

          (a)  The Holder, by acceptance hereof, agrees that this Warrant and
the Shares to be issued upon exercise hereof are being acquired for investment
and that such holder will not offer, sell or otherwise dispose of this Warrant
or any Shares to be issued upon exercise hereof except under circumstances which
will not result in a violation of applicable securities laws.  Upon exercise of
this Warrant, unless the Shares being acquired are registered under the
Securities Act of 1933, as amended (the "Act"), or an exemption from the
                                         ---
registration requirements of such Act is available, the Holder shall confirm in
writing, by executing an instrument in form reasonably satisfactory to the
Company, that the Shares so purchased are being acquired for investment and not
with a view toward distribution or resale. This Warrant

                                       5
<PAGE>

and all Shares issued upon exercise of this Warrant (unless registered under the
Act) shall be stamped or imprinted with a legend in substantially the following
form:

     "THE SECURITIES REPRESENTED BY THIS WARRANT CERTIFICATE AND THE
     SHARES OF STOCK ISSUABLE UPON EXERCISE HEREOF HAVE BEEN ACQUIRED
     FOR INVESTMENT AND HAVE NOT BEEN REGISTERED UNDER THE SECURITIES
     ACT OF 1933, AS AMENDED (THE "ACT"), OR ANY SECURITIES LAWS OF A
                                   ---
     STATE OR OTHER JURISDICTION AND MAY NOT UNDER ANY CIRCUMSTANCES
     BE SOLD, TRANSFERRED OR OTHERWISE DISPOSED OF (OTHER THAN TO AN
     AFFILIATE OR AS OTHERWISE PERMITTED BY THIS WARRANT CERTIFICATE
     PURSUANT TO WHICH THEY WERE ISSUED) EXCEPT PURSUANT TO (i) AN
     EFFECTIVE REGISTRATION STATEMENT UNDER THE ACT AND ANY APPLICABLE
     STATE SECURITIES OR BLUE SKY LAWS, OR (ii) TO THE EXTENT
     APPLICABLE, RULE 144 UNDER THE ACT (OR ANY SIMILAR RULE UNDER THE
     ACT RELATING TO THE DISPOSITION OF SECURITIES) TOGETHER WITH AN
     OPINION OF COUNSEL SATISFACTORY TO INCARA PHARMACEUTICALS
     CORPORATION THAT REGISTRATION IS NOT REQUIRED UNDER THE ACT OR
     APPLICABLE STATE SECURITIES LAWS."

          (b)

               (i)   This Warrant may be transferred or assigned, in whole or in
     part, by EIS to its affiliates and subsidiaries, including any special
     purpose financing or similar vehicle affiliate. Other than as set forth in
     the preceding sentence, this Warrant may not be transferred or assigned by
     either party without the prior written consent of the other. Subject to the
     foregoing, this Warrant and all of the provisions hereof shall be binding
     upon and inure to the benefit of the parties hereto and their respective
     successors and permitted assigns; provided, however, that the transferor
                                       --------  -------
     and the Company shall continue to be liable and obligated for their
     respective obligations hereunder after any such assignment.

               (ii)  With respect to any offer, sale or other disposition of
     this Warrant or any Shares acquired pursuant to the exercise of this
     Warrant prior to registration of such Shares, the Holder shall give written
     notice to the Company prior thereto, describing briefly the manner thereof,
     together with a written opinion of such Holder's counsel, if requested by
     the Company, to the effect that such offer, sale or other disposition may
     be effected without registration or qualification (under the Securities Act
     as then in effect or any federal or state law then in effect) of this
     Warrant or such Shares and indicating whether or not under the Act
     certificates for this Warrant or such Shares to be sold or otherwise
     disposed of require any restrictive legend as to applicable restrictions on
     transferability in order to ensure compliance with the Act. Promptly upon

                                       6
<PAGE>

     receiving such written notice and reasonably satisfactory opinion, if so
     requested, the Company, as promptly as practicable, shall notify such
     Holder that such Holder may sell or otherwise dispose of this Warrant or
     such Shares, all in accordance with the terms of the notice delivered to
     the Company. Each certificate representing this Warrant or the Shares thus
     transferred shall bear a legend as to the applicable restrictions on
     transferability in order to insure compliance with the Securities Act,
     unless in the aforesaid opinion of counsel for the Holder such legend is
     not required in order to insure compliance with the Securities Act. The
     Company may issue stop transfer instructions to its transfer agent in
     connection with such restrictions.

               (iii) The shares of Series B Preferred Stock for which this
     Warrant is exercisable are entitled to the benefit of certain registration
     rights as set forth in that certain Registration Rights Agreement dated as
     of the date hereof between the Company and the initial Holder named herein.

          6.   Rights as Shareholders. No Holder, as such, shall be entitled to
               ----------------------
vote or receive dividends or be deemed the holder of Shares or any other
securities of the Company which may at any time be issuable on the exercise
hereof for any purpose, nor shall anything contained herein be construed to
confer upon the Holder, as such, any right to vote for the election of directors
or upon any matter submitted to shareholders at any meeting thereof, or to
receive notice of meetings, or to receive dividends or subscription rights or
otherwise until this Warrant is exercised and the Shares purchasable upon the
exercise hereof shall have become deliverable, as provided herein.

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

          (a)  The Company has all requisite corporate power and authority to
authorize and execute this Warrant and the certificates evidencing the Shares
and to perform all obligations and undertakings under this Warrant and the
certificates evidencing the Shares;

          (b)  This Warrant has been duly authorized and executed by the Company
and is a valid and binding obligation of the Company enforceable in accordance
with its terms;

          (c)  The Shares have been duly authorized and reserved for issuance by
the Company and, when issued in accordance with the terms hereof, will be
validly issued, fully paid and nonassessable; and

          (d)  The execution and delivery of this Warrant are not, and the
issuance of the Shares upon exercise of this Warrant in accordance with the
terms hereof will not be, inconsistent with the Company's Certificate of
Incorporation or bylaws, as amended, and do not and will not constitute a
default under, any indenture, mortgage, contract or other instrument of which
the Company is a party or by which it is bound.

          8.   Miscellaneous. (a) This Warrant may not be modified or amended,
               -------------
or any provisions hereof waived, except by written agreement of the Company and
the Holder.

                                       7
<PAGE>

          (b)  All notices, demands and requests of any kind to be delivered to
any party in connection with this Note shall be in writing and shall be deemed
to have been duly given if personally or hand delivered or if sent by an
internationally-recognized overnight delivery courier or by registered or
certified mail, return receipt requested and postage prepaid, or by facsimile
transmission addressed as follows:

     (i)  if to the Company, to:

               Incara Pharmaceuticals Corporation
               Post Office Box 14287
               3200 East Highway 54
               Cape Fear Building, Suite 300
               Research Triangle Park, North Carolina 27709
               Attention:  Chief Executive Officer
               Facsimile:  (919) 544-1245

               with a copy to:

               Wyrick Robbins Yates & Ponton LLP
               4101 Lake Boone Trail
               Suite 300
               Raleigh, North Carolina 27607
               Attention:  Larry Robbins
               Facsimile:  (919) 781-4865

     (ii) if to EIS, to:

               Elan International Services, Ltd.
               102 St. James Court
               Flatts, Smiths Parish
               Bermuda FL 04
               Attention:  Chief Executive Officer
               Facsimile:  (441) 292-2224

          with a copy to:

               Brock Silverstein LLC
               800 Third Avenue
               21/st/ Floor
               New York, New York 10022
               Attention:  Kim E. Lefkowitz
               Facsimile:  (212) 371-5500

          (c)  The Company covenants to the Holder that upon receipt of evidence
reasonably satisfactory to the Company of the loss, theft, destruction or
mutilation of this Warrant and, in the case of any such loss, theft or
destruction, upon receipt of a bond or indemnity

                                       8
<PAGE>

reasonably satisfactory to the Company, or in the case of any such mutilation
upon surrender and cancellation of such Warrant, the Company will make and
deliver a new Warrant, of like tenor, in lieu of the lost, stolen, destroyed or
mutilated Warrant.

          (d)  The descriptive headings of the several sections and paragraphs
contained in this Warrant are for reference purposes only and shall not affect
in anyway the meaning or interpretation of this Warrant.

          (e)  This Warrant shall be governed by and construed in accordance
with the internal laws of the State of New York, without giving effect to the
principles of conflicts of laws.  Any dispute under this Warrant that is not
settled by mutual consent may be finally adjudicated by any federal or state
court sitting in the City, County and State of New York, and the Company
consents to the non-exclusive jurisdiction of such courts (or any appellate
court therefrom) over any such dispute. Nothing contained in this Section shall
prevent the adjudication of any dispute under this Warrant by any other state or
federal court, regardless of location, so long as such court has jurisdiction
and is located in a proper venue.

          (f)  This Warrant may be signed and delivered to the other party by a
facsimile transmission; such transmission shall be deemed a valid signature.

          (g)  Each of the parties shall be responsible for its own costs and
expenses incurred in connection with the transactions contemplated hereby.

                           [Signature page follows]

                                       9
<PAGE>

          IN WITNESS WHEREOF, the Company has executed this Warrant as of the
21st day of December, 2000

                               INCARA PHARMACEUTICALS CORPORATION

                               By: /s/ Clayton I. Duncan
                                   ---------------------
                                   Name:  Clayton I. Duncan
                                   Title:  President and Chief Executive Officer
<PAGE>

                                                                         Annex A
                                                                         -------
NOTICE OF EXERCISE
------------------

To:  Incara Pharmaceuticals Corporation

          1.   The undersigned hereby elects to purchase _______ shares of
Series B Preferred Stock of Incara Pharmaceuticals Corporation pursuant to the
terms of the attached Warrant, and tenders herewith full payment of the purchase
price of such shares, in cash or other immediately available funds.

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

____________________________________  (Name)

____________________________________

____________________________________  (Address)

          3.   The undersigned represents that the aforesaid shares are being
acquired for the account of the undersigned for investment and not with a view
to, or for resale in connection with, the distribution thereof and that the
undersigned has no present intention of distributing or reselling such shares.

Signature: ____________________________

Name:      ____________________________

Address:   ____________________________

           ____________________________

           ____________________________


Social Security or taxpayer identification number:

_______________________________________