Algorithms and methods are presented for animating the hands of a synthetic actor. The algorithms allow not only to move the hand and grasp objects, but also to compute deformations of the hand as it moves, for example: rounding at joints and muscle inflations. The mapping of surfaces onto the skeleton is based on the concept of Jointdependent Local Deformation (JLD) operators, which are specific local deformation operators depending on the nature of the joints. The major problem in the hand covering process is the calculation of the coordinate bases. The key to our method was to find a model for calculating the bases which was sophisticated enough for the simulation of complex motions. This model was then improved with additional realistic elements such as muscle inflations and joint roundings. The calculation of the coordinate bases of a vertex in 3-space is separated into two cases: single segment covering for the fingers and two-segment covering for the hand palm. For positioning the hand on an object, three processes are described: the calculation of the distance between a hand vertex and an object, the intersection calculation between the hand and the object and the semiautomatic