Simulating skin deformation relative to a muscle

Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, are disclosed for animations that simulate skin deformation relative to a muscle. Displacement of a skin representation in response to deformation of a muscle representation and sliding of the skin representation over the deformed muscle representation can be determined quickly and interactively by monitoring changes in position and scale of defining ring elements of the muscle representation's geometry. The determined skin displacements can be constrained to prevent portions of the displaced skin representation from sinking into the underlying muscle representation's geometry.