Surgical simulation increasingly appears to be a mandatory aspect of tomorrow's surgery. From today's gesture training, surgical simulators will evolve in order to perform surgical planning with the ability to rehearse the various steps of the operation, thus reducing operating time and risks. In this paper, we describe a virtual environment for surgical training and more specifically a model based on elasticity theory which conveniently links the shape of deformable bodies and the forces associated with the deformation while achieving real time performance.