A 'Family Fun Day' at Cockatoo Island on Sunday ended with patrons shoving and screaming at each other as they waited to get off the island, with ferries unable to cope with the numbers.

The event was jointly organised by the Australian National Maritime Museum and Sydney Harbour Federation Trust.

People attending the Family Fun Day said that some ferries were full upon arrival at the wharf, and families were fighting each other to get on the ferries that were able to take passengers.

Jessica McIntosh took her 14-month-old son to the event and said the scenes at Cockatoo Island on Sunday were frightening.