Historically, predicting ursid feeding behaviour on the basis of morphometric and mechanical analyses has proven difficult. Here, we apply three-dimensional finite element analysis to models representing five extant and one fossil species of bear. The ability to generate high bite forces, and for the skull to sustain them, is present in both the giant panda and the gigantic extinct Agriotherium africanum. Bite forces for A. africanum are the highest predicted for any mammalian carnivore. Our findings do not resolve whether A. africanum was more likely a predator on, or scavenger of, large terrestrial vertebrates, but show that its skull was well-adapted to resist the forces generated in either activity. The possibility that A. africanum was adapted to process tough vegetation is discounted. Results suggest that the polar bear is less well-adapted to dispatch large prey than all but one of the five other species considered.