A 23-year-old surfer has lost an arm and his other hand in a shark attack at a beach near Esperance in southern Western Australia.

The attack happened at Wylie Bay Beach about 11:30am (AWST) on Thursday.

Police have named the man as Sean Pollard from Bunbury.

A spokesman for St John Ambulance said Mr Pollard lost one of his arms in the attack and that his other hand was also torn off.

He was initially taken to hospital in Esperance and was then transferred to the Royal Perth Hospital, by the Royal Flying Doctor Service (RFDS), where he remains in a stable condition.

The manager of the shark response unit at the Department of Fisheries, Lisa Clack, said she believed Mr Pollard was surfing alone, about 150 metres from the surf break.

The department says two sharks have been caught near where the attack occurred.

Ms Clack said two baited drum lines were deployed an hour after the attack, and a great white shark between three and 4.5 metres in length was caught about an hour later.

She said the department had sought permission from the Federal Government to kill the shark.

"On the basis that white sharks of this size are known to have bitten humans, often with fatal consequences, the decision has been made to destroy the shark humanely."

A second great white shark was confirmed captured later Thursday evening.

The department says that even after examination, it may not be possible to determine whether either shark was involved in the attack on Mr Pollard.

Both sharks are being transported to Perth for research purposes.

Shark attack victim Sean Pollard being transferred to Royal Perth Hospital. ( ABC News )

The ABC understands Mr Pollard told authorities he was attacked by two bronze whaler sharks.

Ms Clack said beaches in the area have been closed and are likely to remain closed for several days.

"What I would say, is that I encourage anyone using the water during school holidays to make themselves aware of the latest shark information by checking the Surf Life Saving WA twitter feed, and making an informed decision before they use the beach."

Friends and family send messages of support

Mr Pollard is a member of the South Bunbury Football Club.

Club director Jeff Hayres said the news had come as a shock to the local football community.

"They're devastated. We're all devastated for him. No-one wants to see a 23-year-old in his prime be in this situation. So yeah, everyone at the club's devastated," he said.

In a post on Facebook, the club said: "Our thoughts are with Polly and his family from everyone at South Bunbury Football Club. We are with you all the way mate."

Esperance Shire president Malcolm Heasman said he felt for the victim's family.

"It [the attack] is tragic and my reaction is just initially one of compassion and sympathy not just for the gentleman but also his family who must be going through an horrific time as we speak," he said.

"I am extremely sad but I guess we live in a coastal community so from time to time, unfortunately, these things do happen."

Wylie Bay is an unpatrolled beach about 10 kilometres south-east of Esperance and popular with surfers.

There were seven fatal shark attacks in WA in the three years from 2010 to 2013.

Baited drum lines were deployed off a number of Perth and South-West beaches earlier this year to catch sharks, but plans to extend the trial this summer were abandoned after WA's Environmental Protection Authority advised against it.

Instead, the Government plans to introduce shark barriers at up to 22 beaches, although Esperance beaches are not included in the plans.