Duncan Burgess, 50, was last seen late on the night of Wednesday at the Old Hill Inn in Chapel-le-Dale near Ingleton.
A spokesman for North Yorkshire Police said: "He has no access to a vehicle or money but is physically fit and can walk long distances. He may also be living rough.
"We are particularly appealing to walkers and campers who might have seen him on their travels, including anyone doing the Yorkshire Three Peaks challenge, and to anyone who may have given a lift to Duncan or offered him accommodation in the Yorkshire Dales, Cumbria and Lancashire borders area."
Mr Burgess is described as white with short, dark, brown hair, brown eyes and is of stocky build. He was last seen wearing a red fleece, a blue jacket, dark coloured trousers, a tweed cap and was carrying a large rucksack.
Anyone who has seen him or knows where he is can call North Yorkshire Police on 101 and pass information to the Force Control Room.