The human muscles of mastication have complex shapes with large attachment areas. This suggests a variety of bite force directions and magnitudes. The possible range of these and the concomitant joint force of each individual muscle were determined by a mathematical model describing static equilibrium conditions in the sagittal plane. The range of force directions for each muscle was defined by the action lines of the most anterior and most posterior (for the lateral pterygoid, most superior and most inferior) muscle fibre bundles. Calculations from the various directions of the reaction force in the temporomandibular joint demonstrated that each muscle can produce a unique variety of bite force directions. Except for the lateral pterygoid and posterior temporalis, the range and orientation of possible bite forces was closely related to the orientation of the joint force. In general, at the canine tooth the bite forces were directed more posteriorly than at the second molar. Within a muscle, distinct portions may produce considerably different bite force magnitudes; the largest bite forces are produced at horizontal and vertical joint force directions. The posterior portions of the deep masseter and temporalis muscles and the lateral pterygoid muscle have the largest mechanical advantage. In the majority of muscles the magnitude of the joint reaction force is smallest at an oblique joint force direction.