Despite the large interest in simulators of minimally invasive surgery, it is still unclear to what extent simulators can achieve the task of training medical students in surgical procedures. The answer to that question is certainly linked to the realism of displays and force-feedback systems and to the level of interaction provided by the computer system. In this paper, we describe the virtual environment for anatomical and surgical training on the liver, currently under construction at INRIA. We specifically address the problems of geometric representation and physical modeling and their impact on the two aforementioned problems: realism and real-time interaction.