The results of works about modern materials for implantation in dentistry are presented. Approaches to evaluate the performance efficiency of dental implants, both for single restoration, and for the complete restoration of the entire jaw, with a permanent prosthesis are considered. New forms of implants are being developed, new materials are being used, as well as methods of implantation in the field of dental implantology. In this regard, experts in the field of dentistry often turn to mechanics to evaluate the load-bearing capacity of biomechanical structures. The arising problems don't belong to the number of formalizable problems that can be solved analytically and require the description in three-dimensional form. Therefore, numerical solutions must be used to solve them. The finite element method is the most convenient and often applicable. In this regard, there has been an increase in the number of publications devoted to the determination of the stress-strain state, both prostheses and bone tissue in the area of their fixation. The review of modern articles and books devoted to current researches and trends in the field of dental biomechanics is given.