He is the muscle of the group. A laid-back, tall and powerful bear, he is characterised as having little intelligence. Yet, Square showed intelligence and good will in "Rare Bear Bungle", where he was friendly and trusting of Rare Bear, before Hair showed his suspicions. He has brown fur, and wears a yellow flower-covered blue hat which covers his eyes and a ruby turtleneck shirt.
On the other hand, he has a big appetite, as evidenced in "The Diet Caper", where he is brought to despair after Mr. Peevly bans the bears from getting food. Often his appetite knows no bounds. In "Gobs of Gabaloons", Square Bear bites a lock off a chest after Hair tells him to pretend that it's food.
A running gag is that Square has an invisible motorcycle that he can use whenever or wherever Hair asks him for it so they can use it as a method of nimble escape. He is compassionate and caring, as shown in "Panda Pandamonium", where Square befriends a little panda named Percy, and defends him even after Hair and Bubi are temporarly fed up with it.
He is a fan of professional wrestling, as he mentions in "Goldilocks and the Three Bears". In the same episode, Square indicates that he is a fan of Twinkles Sunshine.