The suspects, who are believed to have targeted elderly shoppers, are thought to have distracted their victims or pretended to help before taking their cards, then withdrawing money.
Several incidents have been reported at Barclays and HSBC in Parliament Street, York, Sainsbury’s in Bootham and Sainsbury’s in Haxby.
They took place on Wednesday, 13 October and Friday 23 October 2015.
York-based PC Ben Hutchinson said: “The offender has observed the victim enter their PIN into the machine before distracting them and removing the card.
“On one occasion an offender has distracted the victim by offering to help them use the cash machine and showing them what button to press.
“The stolen cards were then subsequently used to withdraw money fraudulently.”
He added: “We are doing everything we can to support the victim following this distressing incident.”
Anyone who recognises the men in the photographs or has any other information is urged to contact North Yorkshire Police on 101, ask for Ben Hutchinson and quote incident number 12150188061.
You can also contact Crimestoppers anonymously on 0800 555 111.