In this paper, we describe the basic components of a surgery simulator prototype developed at INRIA. We present two physical models which are well suited for surgery simulation. These models are based on linear elasticity theory and finite elements modeling. The former model can deforme large tetrahedral meshes in real-time but does not allow any topological changes. On the contrary, the latter biomechanical model can simulate the cutting and tearing of soft tissue but must have a limited number of vertices to run in realtime. We propose a method for combining these two approaches into a hybrid model which may allow real time deformations and cuttings of large enough anatomical structures.