Numerous vertebrates exhibit cranial kinesis, or movement between bones of the skull and mandible other than at the jaw joint. Many kinetic species possess a particular suite of features to accomplish this movement, including flexible cranial joints and protractor musculature. Whereas the musculoskeletal anatomy of these kinetic systems is well understood, how these joints are biomechanically loaded, how different soft tissues affect joint loading and kinetic capacity, and how the protractor musculature loads the skull remain poorly understood. Here, we present a finite element model of the savannah monitor, Varanus exanthematicus, a modestly kinetic lizard, to better elucidate the roles of soft tissue in mobile joints and protractor musculature in cranial loading. We describe the 3D resultants of jaw muscles and the histology of palatobasal, otic and jaw joints. We tested the effects of joint tissue type, bite point and muscle load to evaluate the biomechanical role of muscles on the palate and braincase. We found that the jaw muscles have significant mediolateral components that can impart stability across palatocranial joints. Articular tissues affect the magnitude of strains experienced around the palatobasal and otic joints. Without protractor muscle loading, the palate, quadrate and braincase experience higher strains, suggesting this muscle helps insulate the braincase and palatoquadrate from high loads. We found that the cross-sectional properties of the bones of V. exanthematicus are well suited for performing under torsional loads. These findings suggest that torsional loading regimes may have played a more important role in the evolution of cranial kinesis in lepidosaurs than previously appreciated.