In this paper, we present a preliminary study dealing with the importance of correct modeling of connective tissues such as ligaments in laparoscopic liver surgery simulation. We show that the model of these tissues has a significant impact on the overall results of the simulation. This is demonstrated numerically using two different scenarios from the laparoscopic liver surgery, both resulting in important deformation of the liver: insufflation of the abdominal cavity with gas (pneumoperitoneum) and manipulation with the liver lobe using a surgical instrument (grasping pincers). For each scenario, a series of simulations is performed with or without modeling the deformation of the ligaments (fixed constraints or biomechanical model with the parameter of the literature). The numerical comparison shows that modeling the ligament deformations can be at least as important as the correct selection of the patient-specific parameters, nevertheless this observation depends on the simulated scenario.