Exhibit 23.1

INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM’S CONSENT

We consent to the incorporation by reference in this Registration Statement of Pressure Biosciences, Inc. and Subsidiary on Form S-8 of our report dated March 31, 2015, which includes an explanatory paragraph as to the Company’s ability to continue as a going concern, with respect to our audits of the consolidated financial statements of Pressure Biosciences, Inc. and Subsidiary as of December 31, 2014 and 2013 and for the years then endedappearing in the Annual Report on Form 10-K of Pressure BioSciences, Inc. and Subsidiary for the year ended December 31, 2014.

/s/ Marcum llp

Marcum llp

Boston, Massachusetts

April 24, 2015