A modelling approach for the realistic simulation of facial expressions of emotion in craniofacial surgery planning is presented. The method is different from conventional, non-physical techniques for character animation in computer graphics. A consistent physiological mechanism for facial expressions was assumed, which was the effect of contracting muscles on soft tissues. For the numerical solution of the linear elastic boundary values, the finite element method on tetrahedral grids was used. The approach was validated on a geometrical model of a human head derived from tomographic data. Using this model, individual facial expressions of emotion were estimated by the superpositioning of precomputed single muscle actions.