The men were seen on the security cameras at the Askham Bar branch of Tesco allegedly stealing three Dell laptops on the evening of Wednesday 25 January 2012.
It is believed that they secreted the display model computers in a rucksack before leaving the store without making any attempt to pay for them.
Officers are appealing to anyone who can help identify the men to come forward.
PC Pete McFarlane, of York West Safer Neighbourhood Team, said:
I am appealing to anyone who recognises the men in the images to come forward. The pictures are quite clear and I am confident that someone will know who they are.
If you can help identify the men or saw any suspicious activity in the store at the time of the incident, please contact the police or Crimestoppers with information.
I would also ask you to get in touch if you have been offered a laptop for sale in suspicious circumstances recently.
Anyone who can help the investigation is urged to contact North Yorkshire Police on 101 – select option 2 – and ask for PC Pete McFarlane or York police.
Alternatively, Crimestoppers can be contacted anonymously on 0800 555 111, quoting reference number 12120013888.