This paper presents a biomechanical model of the face to simulate orofacial movements in speech and non-verbal communication. A 3D finite element model, based on medical images of a subject, is presented. A hyperelastic Mooney-Rivlin constitutive law accounts for the non-linear behaviour of facial tissue. Muscle fibres are represented by piece-wise uniaxial tensile element that generate force. The stress stiffening effect, an increase in the stiffness of the muscles when activated, is modelled by varying the constitutive law of the tissue with the level of activation of the muscle. A large number of facial movements occurring during speech and facial mimics are simulated. Results show that our modelling approach provides a realistic account of facial mimics. The differences between dynamic vs. quasi-static simulations are also discussed, proving that dynamic trajectories better fit experimental data.