The man, who had on a black skip hat, threatened staff at the Bank of Scotland in Clarkston Road, Clarkston, at around 12.45pm yesterday before making off with thousands of pounds in cash.
Nobody was injured in the incident and they wish to speak to passers-by who may have seen him fleeing into a nearby residential area.
Detective Inspector Alistair Barlow, Community Investigation Unit, said: "Thankfully no one was injured during the robbery; however, it was a very frightening experience for the staff in the bank.
"Our enquiries are still at quite an early stage, however, I would appeal to anyone who was in the area of the bank at the time of the robbery to contact police."
The suspect is white, of medium build and was wearing dark overalls and a black skip hat. He ran off into Cairndow Avenue which leads to a residential area.