The break-in happened at KFC in High Street, Starbeck, at around 1am on December 17.
Two men entered the front of the restaurant, broke into the safe and left via the back of the building.
A North Yorkshire Police spokesman today said: "Officers are asking members of the public to get in touch if they recognise the people in the images as they believe they will have information that will help the investigation."
Anyone with any information is asked to email [email protected] or call the force on on 101, select option 2 and ask for Daniel Fawkes.
Alternatively, call the independent charity Crimestoppers in confidence on 0800 555 111.
Please quote reference number 12180299812 when passing on information.