Although kinematic modelling methods are adequate for describing the shapes of static objects, they are insufficient when it comes to producing realistic animation. Physically based modelling remedies this problem by including forces, masses, strain energies and other physical quantities. The paper describes a system for the animation of deformable models. The system uses physically based modelling methods and approaches from elasticity theory for animating the models. Two different formulations, namely the primal formulation and the hybrid formulation, are implemented so that the user can select the one most suitable for an animation depending on the rigidity of the models. Collision of the models with impenetrable obstacles and constraining of the model points to fixed positions in space are implemented for use in the animations. © 1994.