Abstract The evolution of feeding mechanisms in the ray-finned fishes (Actinopterygii) is a compelling example of transformation in a musculoskeletal complex involving multiple skeletal elements and numerous muscles that power skull motion. Biomechanical models of jaw force and skull kinetics aid our understanding of these complex systems and enable broad comparison of feeding mechanics across taxa. Mechanical models characterize how muscles move skeletal elements by pulling bones around points of rotation in lever mechanisms, or by transmitting force through skeletal elements connected in a linkage. Previous work has focused on the feeding biomechanics of several lineages of fishes, but a broader survey of skull function in the context of quantitative models has not been attempted. This study begins such a survey by examining the diversity of mechanical design of the oral jaws in 35 species of ray-finned fishes with three main objectives: (1) analyze lower jaw lever models in a broad phylogenetic range of taxa, (2) identify the origin and evolutionary patterns of change in the linkage systems that power maxillary rotation and upper jaw protrusion, and (3) analyze patterns of change in feeding design in the context of actinopterygian phylogeny. The mandibular lever is present in virtually all actinopterygians, and the diversity in lower jaw closing force transmission capacity, with mechanical advantage ranging from 0.04 to 0.68, has important functional consequences. A four-bar linkage for maxillary rotation arose in the Amiiformes and persists in various forms in many teleost species. Novel mechanisms for upper jaw protrusion based on this linkage for maxillary rotation have evolved independently at least five times in teleosts. The widespread anterior jaws linkage for jaw protrusion in percomorph fishes arose initially in Zeiformes and subsequently radiated into a wide range of premaxillary protrusion capabilities.