Photos taken of the pair show wounds consistent with their story.
Police are anxious to find security camera footage to corroborate the account and to provide clues about the men's alleged assailants.
The Australians went to a pub in a district known as Chiang Mai Land on Monday night, police were told.
About 6am on Tuesday as they made their way home, the gang of youths attacked them with pieces of wood, the men told police.
They walked on after being assaulted and were helped by monks at Fai temple, the son told officers. The monks sent them to a hospital and the son later reported to a police station.
The men admitted to being drunk at the time they were allegedly assaulted.
A bandaged hand, an abraded face, bandaged head and torso were among the signs of having been beaten up displayed by the younger Australian.
His father appeared to still be in a hospital bed at the time the photographs accompanying this article were taken.
Police contacted by Phuketwan today were unable to remember the names of the two men.
It is not clear whether they have sought consular assistance from the Australian embassy in Bangkok.