Underwater locomotion by plesiosaurs has long been a controversial problem with many hypotheses suggested. Almost without exception these models were based on limited analyses and limited data that failed to adequately examine joint morphology, joint kinematics or test the hypotheses. Our analysis demonstrates that the sea lion- and rowing-models are kinematically impossible due to the prominent glenoid processes that would restrict the necessary posterior motion. Anatomical comparisons with extant tetrapod skeletons show that the glenohumeral joint of plesiosaurs is closest to that of underwater fliers such as sea turtles and penguins. Underwater testing by human swimmers simulating swimming actions of plesiosaurs demonstrate that the most efficient underwater swimming was synchronous and semi-synchronous movements of the fore and hind flippers. These results were supported by computer-generated animations, which showed that semi-synchronous propulsion in which there was a slight lag between fore- and hind limb motion, was the most likely mode of swimming.