In this article, we describe the latest developments of the minimally invasive hepatic surgery simulator prototype developed at INRIA. A key problem with such a simulator is the physical modeling of soft tissues. We propose a new deformable model based on non-linear elasticity, anisotropic behavior, and the finite element method. This model is valid for large displacements, which means in particular that it is invariant with respect to rotations. This property improves the realism of the deformations and solves the problems related to the shortcomings of linear elasticity, which is only valid for small displacements. We also address the problem of volume variations by adding to our model incompressibility constraints. Finally, we demonstrate the relevance of this approach for the real-time simulation of laparoscopic surgical gestures on the liver.