Surgical simulation systems facilitate safe and efficient training processes of surgical trainees by providing a virtual environment in which the surgical procedure can be repeated unlimitedly in a wide variety of situations. The present study attempted to develop a real time simulation system for the grasping procedure of large internal organs during laparoscopic surgery. A mass-spring-damper model was developed to simulate the nonlinear viscoelastic large deformations of the spleen tissue while interacting with a triple-jaw grasper. A novel collision detection algorithm was designed and implemented to determine the contact points between the tissue and the grasper jaws. Force or geometrical based boundary conditions were imposed at the contact nodes, depending upon the relative magnitudes of the external pull force and the tangential component of the contact force. The efficacy of the model to calculate and render the grasper-spleen interactions in real time was examined in a number of simulations. The results of the model were qualitatively acceptable. The deformation of the tissue was realistic and its stress relaxation behavior could be reproduced. Also, the tool-tissue interactions in slippage-free and slippage-accompanied grasping conditions could be replicated when appropriate coefficients of friction were employed.