Muscle contraction is driven by a change in shape of the myosin head region that links the actin and myosin filaments. Tilting of the light-chain domain of the head with respect to its actin-bound catalytic domain is thought to be coupled to the ATPase cycle. Here, using X-ray diffraction and mechanical data from isolated muscle fibres, we characterize an elastic bending of the heads that is independent of the presence of ATP. Together, the tilting and bending motions can explain force generation in isometric muscle, when filament sliding is prevented. The elastic strain in the head is 2.0-2.7 nm under these conditions, contributing 40-50% of the compliance of the muscle sarcomere. We present an atomic model for changes in head conformation that accurately reproduces the changes in the X-ray diffraction pattern seen when rapid length changes are applied to muscle fibres both in active contraction and in the absence of ATP. The model predictions are relatively independent of which parts of the head are assumed to bend or tilt, but depend critically on the measured values of filament sliding and elastic strain.