Some grizzly bears and black bears are able to climb trees. Because of this, it is not wise for someone trying to escape from a bear to climb a tree.
Black bears are good tree climbers. They use their claws to pull themselves up and they even kill opponents by throwing them off of trees. The shorter their claws, the faster they are able to climb. Although adult grizzly bears are not as adept at climbing trees as black bears, they are more likely to do so when going after someone. A person running away from a bear and climbing a tree only provokes the creature to chase him.