Three-dimensional computational modeling offers tools with which to investigate forces experienced by the skull encountered during feeding and other behaviors. American alligators (Alligator mississippiensis) generate some of the highest measured bite forces among extant tetrapods. A concomitant increase in bite force accompanies ontogenetic increases in body mass, which has been linked with dietary changes as animals increase in size. Because the flattened skull of crocodylians has substantial mediolaterally-oriented muscles, they are an excellent model taxon in which to explore the role of mediolateral force components experienced by the feeding apparatus. Many previous modeling studies of archosaur cranial function focused on planar analysis, ignoring the mediolateral aspects of cranial forces. Here we use three-dimensionally accurate anatomical data to resolve 3D muscle forces. Using dissection, imaging, and computational techniques, we developed lever and finite element models of an ontogenetic series of alligators to test the effects of size and shape on cranial loading and compared estimated bite forces to those previously measured in vivo in Alligator mississippiensis We found that modeled forces matched in vivo data well for intermediately sized individuals, and somewhat overestimated force in smaller specimens and underestimated force in larger specimens, suggesting that ontogenetically static muscular parameters and bony attachment sites alone cannot account for all the variation in bite force. Adding aponeurotic muscle attachments would likely improve force predictions, but such data are challenging to model and integrate into analyses of extant taxa and are generally unpreserved in fossils. We conclude that anatomically accurate modeling of muscles can be coupled with finite element and lever analyses to produce reliable, reasonably accurate estimate bite forces and thus both skeletal and joint loading, with known sources of error, which can be applied to extinct taxa.