This paper addresses the problem of grasping rigid and deformable objects in a task-level animation system. After an introduction on task planning and grasping, it emphasizes the use of FEM for modelling both elastically and plastically deformations of objects, and impacts with or without penetration between deformable objects. A numerical method based on finite element theory allows us to take into account the active forces of the fingers on the object and the reactive forces of the object on the fingers