We focus on motor control underlying lip protrusion and rounding in speech production using modelling approach. A finite element model has been used and muscle behaviour has been modelled by two types of elements. 3D link elements have been used for the representation of the active part of muscle force. The surrounding elements of these link elements in the main mesh describe the anatomical location of the muscles. Since muscles generate tensile internal force which is associated with stress stiffening, muscle activation in the model generates a functional change of material properties of those surrounding elements. The passive part of muscle is inherently taken into account by the mechanical properties of the main mesh. It is shown that considering the effect of stiffening facilitates co-occurence of rounding and protruding and corresponds to more realistic face gestures. The sensitivity analysis of lip shaping parameters due to change in stiffness has been used to quantitatively assess the role of these mechanical properties. In addition the study of the effects of different muscles on lip protrusion and rounding have revealed that to give better account of experimental observation the mentalis muscle should be activated in parallel to the orbicularis oris muscle: which is in good agreement with anatomical facts.