Exhibit 31.1

# Certification by Chief
Executive Officer Pursuant to Section 302 of the

# Sarbanes-Oxley Act of
2002

I, Joseph Ackerman,
certify that:

|1. | I have reviewed this annual report on Form 20-F of Elbit Systems Ltd.
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|2. | Based on my knowledge, this annual 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 annual report.
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|3. | Based on my knowledge, the financial statements, and other financial information
          included in this annual 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 annual report.
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|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 have:
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|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;
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|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 on such evaluation; and
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|c) |  | disclosed in this report any change in the registrants internal control
                    over financial reporting that occurred during the registrants most recent
                    fiscal quarter (the registrants fourth fiscal quarter in the case of an
                    annual report) that has materially affected, or is reasonably likely to
                    materially affect, the registrants internal control over financial
                    reporting.
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|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 the registrants
          board of directors (or persons performing the equivalent functions):
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|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
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|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.
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Date: June 28, 2006

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| |  | -------------------------------------------------------------- | 
| | 
| |  | /s/ Joseph Ackerman                                            | 
| |  | Joseph AckermanPresident, Chief Executive Officer and Director | 
| |