Exhibit 31.1



CERTIFICATION BY PRINCIPAL EXECUTIVE
OFFICER

UNDER SECTION 302 OF THE SARBANES–OXLEY
ACT OF 2002



I, Anthony Angelini, certify that:



1. I have reviewed this Quarterly Report on Form 10-Q of TSS,
Inc.;



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 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)) and internal control over financial reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant
and 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) designed such internal control over financial reporting,
or caused such internal control over financial reporting to be designed under our supervision, to provide reasonable assurance
regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance
with generally accepted accounting principles;



(c) 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



(d) 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; 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 the registrant’s board of directors (or person performing the equivalent functions):



(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.



|August 14, 2013 | By: | /s/ Anthony Angelini         
|--------------- | --- | -----------------------------
|                |     | Anthony Angelini             
|                |     | Chief Executive Officer      
|                |     | (Principal Executive Officer)