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**Exhibit 31.2**

**CERTIFICATION OFCHIEF FINANCIAL OFFICERSection 302 Certification**

I, Kenneth J.Galaznik, certify that:

1.                  Ihave reviewed this quarterly report on Form 10-Q of American Science andEngineering, Inc.;

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

3.                  Basedon my knowledge, the financial statements, and other financial informationincluded in this report, fairly present in all material respects the financialcondition, results of operations and cash flows of the registrant as of, andfor, the periods presented in this report;

4.                  Theregistrant’s other certifying officer and I are responsible for establishingand maintaining disclosure controls and procedures (as defined in Exchange ActRules 13a-15(e) and 15d-15(e)) and internal control over financialreporting (as defined in Exchange Act rules 13a-15(f) and 15d-15(f))for the registrant and have:

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

b)               Designedsuch internal control over financial reporting, or caused such internal controlover financial reporting to be designed under our supervision, to providereasonable assurance regarding the reliability of financial reporting and thepreparation of financial statements for external purposes in accordance withgenerally accepted accounting principles;

c)                Evaluatedthe effectiveness of the registrant’s disclosure controls and procedures andpresented in this report our conclusions about the effectiveness of thedisclosure controls and procedures, as of the end of the period covered by thisreport based on such evaluation; and

d)               Disclosedin this report any change in the registrant’s internal control over financialreporting that occurred during the registrant’s most recent fiscal quarter thathas materially affected, or is reasonably likely to materially affect, theregistrant’s internal control over financial reporting;

5.                  Theregistrant’s other certifying officer and I have disclosed, based on our mostrecent evaluation of internal control over financial reporting, to theregistrant’s auditors and the audit committee of the registrant’s board ofdirectors (or persons performing the equivalent functions):

a)                Allsignificant deficiencies and material weaknesses in the design or operation ofinternal control over financial reporting which are reasonable likely toadversely affect the registrant’s ability to record, process, summarize andreport financial information; and

b)               Anyfraud, whether or not material, that involves management or other employees whohave a significant role in the registrant’s internal control over financialreporting.
| Date: August 9, 2006              |   |
|----------------------------------------|--------|
|                                   |   |
| /s/ Kenneth J.  Galaznik               |   |
| Kenneth J.  Galaznik                   |   |
| Chief Financial  Officer and Treasurer |   |

 

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