The families of four Australian travellers whose boat has gone missing off the Indonesian coast are holding out hope they will be found alive.

A search operation is underway for Elliot Foote, Steph Weisse, Will Teagle and Jordan Short who were heading to a “hidden paradise” of white beaches and epic surf.

They were among seven riding a wooden speedboat to Pinang Island, on the western tip of Sumatra, during bad weather with heavy rain.

Their boat, which set out on Sunday afternoon, never arrived.

The young surfers’ families issued a statement late Monday. The group was reportedly on a holiday celebrating Elliot’s 30th birthday.

“Our hearts are aching at the thought that Elliot, Steph, Will and Jordan are missing at sea,” it said.

“We continue to pray and hold out hope they will be found.”

A total of 12 Australian nationals and five Indonesians were travelling to the surf island in two separate boats on Sunday afternoon.

Ten of them decided to stay and shelter on Sarang Alu island, while the others continued the trip.

The resort on Pinang Island later reported that only one of the boats with 10 passengers had safely arrived.

The boat that had left earlier with the missing Australians on board had not been seen.

Pinang Island is billed as a “castaway” haven and adventure paradise near the Bay of Plenty surf location.

Hours before they vanished, Elliot posted to Instagram about the trip so far.

“Soho gulah Sorake … so good being back in Indo after so many years. Sharing waves with mates and the queen,” he wrote, referring to girlfriend Steph.

“Starting the trip off with hiking in the North Sumatran jungle and seeing orangutan’s was an amazing experience and something that I look forward to doing again for a longer time and going deeper.”

A resort owner, Julian Lauencoan, told the ABC he believed the missing wooden boat was unlikely to sink.

He also said the weather had improved and, given the direction of the winds, they would not have been blown out to sea.

“The wind was not easterly, which would push it to the Indian Ocean, but would instead push it west back to land,” he told the ABC.

“It can happen: I have heard a couple of stories like this where they would spend a few days at sea, but once they come close to land fishermen find them.”

“They have water and food on the boat, so they’ll be OK for a few days.”

Pinang Island is a secluded tropical paradise popular with surfers. Photo: Pinangisland.com

Rescuers were sending at least two rescue boats and a medical boat to the search waters around Sarang Alu and Banyak islands in Aceh Singkil district.

The boat carrying the Australian tourists is understood to have disappeared off the western Aceh province on Monday.

The Department of Foreign Affairs and Trade confirmed it was working closely with Indonesian authorities to support search and rescue efforts.

The department was also providing consular assistance to the four families, a spokeswoman told AAP.

Indonesia is an archipelago with more than 17,000 islands, and ferries and boats are a common form of transportation.

With lax safety standards and problems with overcrowding, accidents occur frequently.

Authorities have begun a search and rescue operation for Australians missing off the coast of Aceh. Photo: AAP

In July, an overloaded passenger boat capsized off Indonesia’s Sulawesi island, killing 15 people.

In 2018, an overcrowded ferry with about 200 people on board sank in a lake in North Sumatra province, killing 167 people.

In one of the country’s worst recorded disasters, an overcrowded passenger ship sank in February 1999 with 332 people aboard. Only 20 people survived.