The skull and mandible of the type specimen of the large pliosauroid plesiosaur Rhomaleosaurus zetlandicus from the Toarcian of England are elongate, and adapted for powerful predatory activity in water. The mandible contains all elements found in primitive reptilian mandibles. The broadly caniniform dentition suggests that Rhomaleosaurus fed on a wide range of active prey, and forcibly dismembered larger prey by shaking and twisting them. The cranial musculature is reconstructed for the first time in plesiosaurs. It was adapted for feeding in water. The adductor musculature included a large anterior pterygoideus attached to the suborbital fenestra, a large posterior pterygoideus, and a group of large dorsal muscles including the adductor mandibulae externus. The anterior pterygoideus exerted maximum torque when the jaws were wide open, snapping them shut quickly, and the dorsal muscle mass exerted maximum torque when the jaws were closed on prey to subdue and dismember it. The role of the posterior pterygoideus is uncertain or intermediate. The musculature combines elements of the `kinetic inertial' system ascribed to aquatic tetrapods by Olson (1961), with his `static pressure' system ascribed to terrestrial tetrapods. Olson suggested that the large pterygoideus musculature typical of the `kinetic intertial' system functioned to confer kinetic energy on the mandible. However, its function may instead have been to compensate for the inertia and drag of the mandible. The depressor musculature comprised the depressor mandibulae and the longitudinal pharyngeal muscles, and opened the jaw quickly against drag. The cervical musculature cannot be reconstructed in detail. There was a strong nuchal ligament. The forces within the head are analysed by using box and girder beams as analogues. Gross form, shape of constituent bones, and sutural morphology confirm adaptations to resist great bending moments arising from the action of the muscles when biting on prey. When the jaws were closed, the pterygoid flange supported the mandible against the inward component of the adductor muscle force. Rhomaleosaurus was a visual predator. The eyes were large. The stapes is present. Underwater olfaction was likely. There is no evidence for an eardrum, but it is not known whether this is the plesiomorphic reptilian state or secondarily derived from a tympanate ancestor. The ears were not acoustically isolated from the braincase, so underwater directional hearing was poor, and sonar was not possible. The structure of the head of Rhomaleosaurus is a functional compromise between the needs to maximize structural strength and to maximize swimming and feeding efficiency. Especially important were the ability to sustain large muscle and reaction forces to provide an adequate bite force at the end of a long snout, and the wide gape allowing the swallowing of large picces of prey. Even larger items were dismembered into smaller pieces by shake and twist feeding. The major unresolved problems are the effects of scaling factors, and the torsional loadings induced when biting asymmetrically, or twisting large prey to pieces.