This paper presents the biomechanical finite element models that have been developed in the framework of the computer-assisted maxillofacial surgery. After a brief overview of the continuous elastic modelling method, two models are introduced and their use for computer-assisted applications discussed. The first model deals with orthognathic surgery and aims at predicting the facial consequences of maxillary and mandibular osteotomies. For this, a generic three-dimensional model of the face is automatically adapted to the morphology of the patient by the mean of elastic registration. Qualitative simulations of the consequences of an osteotomy of the mandible can thus be provided. The second model addresses the Sleep Apnoea Syndrome. Its aim is to develop a complete modelling of the interaction between airflow and upper airways walls during breathing. Dynamical simulations of the interaction during a respiratory cycle are computed and compared with observed phenomena.