The robbery took place at Tesco Express, Kilnhouse Lane, at about 1pm.
Detectives are appealing for witnesses to the incident.
Police said a silver machete was brandished during the attack.
Fortunately nobody was injured, although the victim was left badly shaken.
The amount of money stolen has not bee disclosed.
The three men escaped in a silver Mercedes saloon in the direction of the promenade.
Driven by a fourth man, the vehicle was found abandoned along Eaves Road, near to the Harvester pub.
The car has been recovered and scenes of crime officers are now examining the vehicle.
The men are then believed to have escaped into a small white van.
The police helicopter was scrambled.
An eyewitness, who lives near the store and who asked not to be named, told the Express: "I heard this screech. This is a very busy place. You are always hearing people shouting.
"I saw a car reverse back while the Securicor car's doors opened up.
"All I could think of doing was taking the first four letters of the registration.
"I rang the police. It is not the sort of thing you expect to happen.
"The next thing, the car sped off."
The witiness said she saw the raiders.
"They all had ski masks and dark clothes. I saw one with something in their hand. It wasn't a gun.
"Nobody was coming out of Tesco. My main concern was somebody might have been hurt.
"Can you imagine children going into the shop for their mums and dads. Can you imagine how horrible it would have been for them.
"It all happened so quickly, within a minute. We have never had anything like this before. It's a shock. I'm still coming back down."
The woman said there used to be a CCTV camera on the end of the store, but that it was "hanging off" and taken down. She said the raiders may have known this.
Police said one of the offenders is described as about 20-years-old, of slim build, with a shaved head. They have no further descriptions of the men at this time.
Detective Chief Inspector Andy Webster said: "We are appealing to anyone with any information about this robbery to come forward and contact police.
"I would be particularly interested to speaking to anyone who saw the robbery itself or noticed anybody acting strangely around Kilnhouse Lane area either today, or in the days leading up to the incident.
"We are also keen to identify where the car and its occupants have been before, during and after the offence. "
Anyone with information should contact the police on 08451 25 35 45 or call Crimestoppers anonymously on 0800 555 111.