Calls to cull sharks are growing louder after a woman was critically injured by a shark at one of Australia's best-known beaches.

Suffering severe injuries to her limbs, the woman was airlifted to hospital for immediate treatment.

A woman in her 30s is being treated by NSW Ambulance after being bitten by a shark at the eastern suburbs beach.

A woman has been attacked by a shark at Sydney's popular Coogee Beach.