They threatened the elderly shopkeeper and a member of staff with weapons and demanded money during the incident in Nazir's Newsagents in Craigbank Drive, Pollok.
A 62-year-old female employee and the 74-year-old shopkeeper were left "terrified" but unharmed, police said.
The two men left empty handed after the shopkeeper managed to chase them from the store following the incident at 6.30am, yesterday. They ran away, possibly across Nitshill Road.
Detective Constable Neil Guy, from the Community Investigation Unit in Pollok, has launched an appeal for information.
The suspects are described as white, in their early 20s and were wearing black clothing.
Anyone with information should call Pollok Police Office on 101.