We propose three physical models based on linear elasticity theory and finite-element modeling that are well-suited for surgery simulation. The first model combines precomputed deformations to deform large size meshes in real-time, but cannot make any topological changes to the mesh. The second model is similar to the spring-mass models where volumetric deformations and cutting operations can be simulated on small meshes in real time. Finally, we have developped a third method, combining the previous two solutions into a hybrid model that simulates deformations and cutting on complex anatomical structures.