In this presentation, we describe the basic components of a surgery simulator prototype developed at INRIA. After a short presentation of the geometric modeling of anatomical structures from medical images, we insist on the physical modeling components which must allow realistic interaction with surgical instruments. We present three physical models which are well suited for surgery simulation. Those models are based on linear elasticity theory and finite elements modeling. The first model pre-computes the deformations and forces applied on a finite element model, therefore allowing the deformation of large structures in real-time. Unfortunately, it does not allow any topology change of the mesh therefore forbids the simulation of cutting during surgery. The second physical model is based on a dynamic law of motion and allows to simulate cutting and tearing. We called this model «tensor-mass» since it is analogous to spring-mass models for linear elasticity. This model allows volumetric deformations and cuttings, but has to be applied to a limited number of nodes to run in real-time. Finally, we propose a method for combining those two approaches into a hybrid model which may allow real time deformations and cuttings of large enough anatomical structures. We present preliminary results and conclude with perspectives.