<PAGE>
                       THE LUBRIZOL CORPORATION                       Exhibit 31
                    Rule 13a-14(a) Certification

I, William G. Bares, certify that:

1. I have reviewed this annual report on Form 10-K of The Lubrizol Corporation;

2. Based on my knowledge, this report does not contain any untrue statement of a
material fact or omit to state a material fact necessary to make the statements
made, in light of the circumstances under which such statements were made, not
misleading with respect to the period covered by this report;

3. Based on my knowledge, the consolidated financial statements, and other
financial information included in this report, fairly present in all material
respects the financial condition, results of operations and cash flows of the
registrant as of, and for, the periods presented in this report;

4. The registrant's other certifying officer and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant and we have:

   a) designed such disclosure controls and procedures, or caused such
   disclosure controls and procedures to be designed under our supervision,
   to ensure that material information relating to the registrant, including
   its consolidated subsidiaries, is made known to us by others within those
   entities, particularly during the period in which this report is being
   prepared;

   b) evaluated the effectiveness of the registrant's disclosure controls and
   procedures and presented in this report our conclusions about the
   effectiveness of the disclosure controls and procedures, as of the end of
   the period covered by this report based upon such evaluation;

   c) disclosed in this report any change in registrant's internal control
   over financial reporting that occurred during registrant's most recent
   fiscal quarter that has materially affected, or is reasonably likely to
   materially affect, the registrant's internal control over financial
   reporting; and

5. The registrant's other certifying officer and I have disclosed, based on our
most recent evaluation of internal control over financial reporting, to the
registrant's auditors and the audit committee of registrant's board of directors
(or persons performing the equivalent function):

   a) all significant deficiencies and material weaknesses in the design or
   operation of internal control over financial reporting which are
   reasonably likely to adversely affect the registrant's ability to record,
   process, summarize and report financial information; and

   b) any fraud, whether or not material, that involves management or other
   employees who have a significant role in the registrant's internal control
   over financial reporting.





       /s/ William G. Bares
---------------------------
William G. Bares
Chief Executive Officer
February 18, 2004


<PAGE>

                       THE LUBRIZOL CORPORATION                       Exhibit 31
                    Rule 13a-14(a) Certification

I, Charles P. Cooley, certify that:

1. I have reviewed this annual report on Form 10-K of The Lubrizol Corporation;

2. Based on my knowledge, this report does not contain any untrue statement of a
material fact or omit to state a material fact necessary to make the statements
made, in light of the circumstances under which such statements were made, not
misleading with respect to the period covered by this report;

3. Based on my knowledge, the consolidated financial statements, and other
financial information included in this report, fairly present in all material
respects the financial condition, results of operations and cash flows of the
registrant as of, and for, the periods presented in this report;

4. The registrant's other certifying officer and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant and we have:

   a) designed such disclosure controls and procedures, or caused such
   disclosure controls and procedures to be designed under our supervision,
   to ensure that material information relating to the registrant, including
   its consolidated subsidiaries, is made known to us by others within those
   entities, particularly during the period in which this report is being
   prepared;

   b) evaluated the effectiveness of the registrant's disclosure controls and
   procedures and presented in this report our conclusions about the
   effectiveness of the disclosure controls and procedures, as of the end of
   the period covered by this report based upon such evaluation;

   c) disclosed in this report any change in registrant's internal control
   over financial reporting that occurred during registrant's most recent
   fiscal quarter that has materially affected, or is reasonably likely to
   materially affect, the registrant's internal control over financial
   reporting; and

5. The registrant's other certifying officer and I have disclosed, based on our
most recent evaluation of internal control over financial reporting, to the
registrant's auditors and the audit committee of registrant's board of directors
(or persons performing the equivalent function):

   a) all significant deficiencies and material weaknesses in the design or
   operation of internal control over financial reporting which are
   reasonably likely to adversely affect the registrant's ability to record,
   process, summarize and report financial information; and

   b) any fraud, whether or not material, that involves management or other
   employees who have a significant role in the registrant's internal control
   over financial reporting.



     /s/ Charles P. Cooley
--------------------------
Charles P. Cooley
Chief Financial Officer
February 18, 2004