Aslan King, 25, has been missing since the early hours of Saturday morning after suffering what friends have described as possibly a form of seizure during a coastal camping trip.
Mr King, an illustrator from Brighton who only relocated to Australia two weeks ago, is said to have hit his head on the ground before getting up quickly and rushing into thick bushland surrounding the campsite where he and four friends had been staying.
The site is near the town of Princeton, beside cliffs on the Victorian coast near the tourist site known as the Twelve Apostles, a series of rocky outcrops rising out of the ocean some 100 miles south-west of Melbourne.
Victoria Police said officers were searching for Mr King on Sunday using a helicopter, horses, motorcycles and sniffer dogs.
Local media also showed water-borne police officers checking along the coastline in rubber dinghies.
Police told local media they were concentrating on a radius of 300 metres around the campsite, but said the search was difficult because of the thick vegetation, rocky clifftops and deep water coastal waters in the region.
The area is also known to contain a large population of deadly tiger snakes.
Sergeant Danny Brown of Victoria Police said thermal imaging sensors used on Saturday and Sunday had detected no trace of Mr King, but that they might be used again as the search continued on Sunday night.
"You're using every sense, whether that be eyes, ears and touch as well," he told Nine newspapers, adding the heat sensors would make "a massive difference, because we're going to find things in areas that the eye can't see".
"Some of this scrub, you have to get on hands and knees to move through it," he said.
Sgt Brown said Mr King's friends and family had described his disappearance as "completely out of character".
The Foreign Office said in a statement: "Our staff are seeking further information following the disappearance of a British man near Princeton, Australia and are in contact with the Australian police."