Mathematical modelling is being used in modern dentistry to solve a wide range of scientific problems. The models allow one to predict and estimate the medical intervention impact during the calculations of stress-strain state of prostheses and medical devices. In the present research a mathematical model of the lower jaw, considering the individual characteristics of the geometry, properties of bone tissue and activity of the patient’s mastication muscles using the finite element method is proposed. The work provides an example of determining the operational characteristics of dentoalveolar structures. The analysis of displacements, tensions, and deformations for a particular tooth as well as the selection of the implant diameter were presented as results.