A quantitative stochastic model of the mechanochemical cycle of myosin, the protein that drives muscle contraction, is proposed. It is based on three premises: (i) the myosin head incorporates a lever arm, whose equilibrium position adjusts as each of the products of ATP hydrolysis dissociates from the nucleotide pocket; (ii) the chemical reaction rates are modified according to the work done in moving the arm; and (iii) the compliance of myosin's elastic element is designed to permit many molecules to work together efficiently. The model has a minimal number of parameters and provides an explanation, at the molecular level, of many of the mechanical and thermodynamic properties of steadily shortening muscle. In particular, the inflexion in the force-velocity curve at a force approaching the isometric load is reproduced. Moreover, the model indicates that when large numbers of myosin molecules act collectively, their chemical cycles can be synchronized, and that this leads to stepwise motion of the thin filament. The oscillatory transient response of muscle to abrupt changes of load is interpreted in this light.