Police in Perth say experts believe missing swimmer Bryn Martin was taken by a white pointer shark at Cottesloe Beach.

The 64-year-old Mosman Park man set out from the shore near the Indiana Tea Rooms on his daily swim on Monday morning.

He was heading out to a buoy several hundred metres from the shore when he disappeared from sight.

A friend and several other swimmers went into the water looking for Mr Martin but could find no sign of him.

Senior Sergeant Denise Grant says several hours later, police divers found Mr Martin's bathers on the sea bed near the buoy.

"Police divers have located a pair of black speedo bathers that have been positively identified by our missing person's wife," she said.

Police say fisheries experts have viewed the bathers and say the damage to them is consistent with that which a white pointer shark would cause.

Senior Sergeant Denise Grant says Mr Martin's friend quickly alerted authorities.

"He comes down with a friend and his friend was waiting on the beach and he saw him swimming out there, and then he's gone to enter the water and then he couldn't see him anymore," she said.

"He was a very strong and a very good swimmer apparently."

Mr Martin's family spent the day at the beach waiting for developments.

The skipper of a Whitfords sea rescue boat involved in the search, Mike Walters, has told the ABC it was thorough.

"It was fairly intense and there were a couple of helicopters in the air and the police helicopter was there for a very long period of time, so they gave it the best chance," he said.

Police, surf lifesavers and SAS troops from the nearby barracks spent the day searching the water and foreshore for the man.

Police spokesman Graeme Clifford says Mr Martin is a regular swimmer at Cottesloe.

"He was due to meet his family a short time after; he didn't return," he said.

The beach has been closed until further notice.