Proposed creatures

Various types of creature have been described by proponents to explain the sightings. These descriptions have received little support from the scientific community.

Gigantopithecus
Grover Krantz argued that a relict population of Gigantopithecus blacki would best explain Bigfoot reports. Based on his fossil analysis of its jaws, he championed a view that Gigantopithecus was bipedal.
Bourne writes that Gigantopithecus was a plausible candidate for Bigfoot since most Gigantopithecus fossils were found in China, whose extreme eastern Siberian forests are similar to those of north-western North America. Many well-known animals have migrated across the Bering Strait, so it was not unreasonable to assume that Gigantopithecus might have as well. "So perhaps," Bourne writes, "Gigantopithecus is the Bigfoot of the American continent and perhaps he is also the Yeti of the Himalayas" (Bourne, 296).
The Gigantopithecus hypothesis is generally considered highly speculative. Given the mainstream view that Gigantopithecus was quadrupedal, it would seem unlikely to be an ancestor to the biped Bigfoot is said to be. Moreover, it has been argued that G. blacki's enormous mass would have made it difficult for it to adopt a bipedal gait. An analysis of the Patterson-Gimlin film shows that frames 369, 370, 371, and 372 all show a slender lower mandible, that does not match the massive lower mandible of Gigantopithecus blacki, which, assuming that the Patterson-Gimlin film is legitimate, would eliminate G. blacki as a candidate for Bigfoot. (Bigfoot Coop Newsletter, March 1997, also the documentary Sasquatch: Legend Meets Science).
"That Gigantopithicus is in fact extinct has been questioned by those who believe it survives as the Yeti of the Himalayas and the Sasquatch of the north-west American coast. But the evidence for these creatures is not convincing." (Campbell p.100)

Other extinct apes
A species of Paranthropus, such as Paranthropus robustus, with its crested skull and bipedal gait, was suggested by Napier and anthropologist Gordon Strasenburg as a possible candidate for Bigfoot's identity.
Some Bigfoot reports suggest Homo erectus to be the creature, but H. erectus skeletons have never been found on the North American continent.
There was also a little known genus, called Meganthropus, which reputedly grew to enormous proportions. Again, there have been no remains of this creature anywhere near North America, and none younger than a million years old.