Bite marks suggest that the late Eocence archaeocete whale Basilosaurus isis (Birket Qarun Formation, Egypt) fed upon juveniles of the contemporary basilosaurid Dorudon atrox. Finite element analysis (FEA) of a nearly complete adult cranium of B. isis enables estimates of its bite force and tests the animal's capabilities for crushing bone. Two loadcases reflect different biting scenarios: 1) an intitial closing phase, with all adductors active and a full condylar reaction force; and 2) a shearing phase, with the posterior temporalis active and minimized condylar force. The latter is considered probable when the jaws were nearly closed because the preserved jaws do not articulate as the molariform teeth come into occulusion. Reaction forces with all muscles active indicate that B. isis maintained relatively greater bite force anteriorly than seen in large crocodilians, and exerted a maximum bite force of at least 16,400 N at its upper P3. Under the shearing scenario with minimized condylar forces, tooth reaction forces could exceed 20,000 N despite lower magnitudes of muscle force. These bite forces at the teeth are consistent with bone indentations on Dorudon crania, reatract-and-shear hypotheses of Basilosaurus bite function, and seizure of prey by anterior teeth as proposed for other archaeocetes. The whale 's bite forces match those estimated for pliosaurus when skull lengths are equalized, suggesting similar tradeoffs of bite function and hydrodynamics. Reaction forces in B. isis were lower than maxima estimated for large crocodylians and carnivorous dinosaurs. However, comparison of force estimates from FEA and regression data indicate that B. isis exerted the largest bite forces yet estimated for any mammal, and greater force than expected from its skull width. Cephalic feeding biomechanics of Basilosaurus isis are thus consistent with habitual predation.