Amoeboid cells crawl by simultaneously extending lamellipodia and retracting their cell bodies. A precise mechanical analysis of this process has been difficult because, in most cases, locomotion is generated by the actin cytoskeleton, which is also involved in many other processes. George Oster and co-workers have approached the problem by analyzing a ‘stripped down’ version of a crawling cell: sperm from the nematode Ascaris suum. These cells crawl using a unique cytoskeletal filament system based on the major sperm protein (MSP), which is dedicated to locomotion and requires few accessory proteins. The authors have developed a computational model that accounts for the principal features of crawling in terms of vectorial filament assembly and bundling without a major contribution from motor proteins. In the model, localized filament polymerization/bundling at the leading edge of lamellipodia generates protrusive force; this is coupled to localized contraction at the cell body, which is generated by relief of tensile stress through pH-dependent filament depolymerization. Oster and co-workers show that their model accurately simulates key aspects of sperm motility, such as velocity and cell shape, thus providing a theoretical framework for understanding the molecular basis of cell motility.