Organ motion due to respiration and contact with surgical instruments can significantly degrade the accuracy of image guided surgery. In most applications the ensuing soft tissue deformations have to be compensated in order to register preoperative planning data to the patient. Biomechanical models can be used to perform an accurate registration based on sparse intraoperative sensor data. Using elasticity theory, the approach can be formulated as a boundary value problem with displacement boundary conditions. In this paper, several models of the liver from the literature and a new simplified model are evaluated with regards to their application to intraoperative soft tissue registration. We construct finite element models of a liver phantom using the different material laws. Thereafter, typical deformation pattern that occur during surgery are imposed by applying displacement boundary conditions. A comparative numerical study shows that the maximal registration error of all non-linear models stays below 1.1mm, while the linear model produces errors up to 3.9mm. It can be concluded that linear elastic models are not suitable for the registration of the liver and that a geometrically non-linear formulation has to be used. Although the stiffness parameters of the non-linear materials differ considerably, the calculated displacement fields are very similar. This suggests that a difficult patient-specific parameterization of the model might not be necessary for intraoperative soft tissue registration. We also demonstrate that the new simplified model achieves nearly the same registration accuracy as complex quasi-linear viscoelastic models.