The objective of this study was to investigate distribution of stresses in the human TMJ discs, generated during clenching into various occlusal positions. The work presents a biomechanical finite element model of interaction of mandibular and maxillary dental arches and the TMJ discs of a particular person, based on real geometrical data obtained from spiral computed tomography two-dimensional images. 3D contour coordinates - point clouds were collected from these images and solid model was created. The system under investigation consisted of eight basic parts: two rigid structures representing the mandibular and maxillary dental arches, two mandibular condyles, two mandibular fossae of temporal bone, and solid models of two articular discs. The model of maxillary dental arch was fixed in space. The model of the mandibular dental arch was able to move in space synchronically with the mandibular condyles under action of applied forces, which were considered as prescribed and known at insertion points of masticatory muscles. The motion of the mandible was constrained by interdental contact interactions and contact interaction with articular discs, which were situated in between mandibular condyles and mandibular fossae of temporal bone. The model was implemented by using LS-DYNA finite element software. The obtained results presented a 3D view of stresses exhibited in the articular discs, as well as the real contact points of dental interactions at given masticatory geometry of a particular subject and the values of interaction forces. The expected practical value of the developed model is the facilitation of biomechanical evaluations of the influence of tolerances of teeth shapes and occlusal areas together with the supporting areas on the final stress distribution in the dental arches and articular discs.