The aim of the study was to improve the effectiveness of orthopedic treatment for patients with dentition defects by method of making a removable denture with claspless fixation, taking into account the mathematical modelling of the teeth and undercut inclination. The technique of making claspless partial dentures by using A-silicone material is based on the idea of using the elastic forces generated in the wedge-shaped body of elastic material under the influence of an external force, which resets the prosthesis. Based on the considerations, it was developed a scheme of the claspless denture model and the mathematical modeling of partial removable laminar dentures fixation with elastic material, resulting in the special formula. After analyzing the results, we suggest to use in the clinic simplified table. With their help, you can easily determine the rationality of claspless denture, which is planned to produce on the technology that we offer. For this, you need to determine the ratio of the magnitude undercut and height of the inclined teeth and to compare them with the data tables. The most efficient should be considered claspless design of the prosthesis, if both of the inclined abutments have a ratio of the magnitude of undercut and height not less than the value of the ratio when the value F/2=0.3 kg U= 1 mm. In this case, it can be argued that claspless prosthesis under the influence of dropping efforts 0,3 kg will move in the vertical direction not more than 0.5 mm, and under the influence dropping efforts to 0.6 kg not more than 1 mm. But, if one or both of the sloping supporting the tooth have the ratio of the magnitude undercut and a height of about one (an angle of about 45°), then there will be difficulties with the insertion of claspless denture on the prosthetic bed. Thus, the fixation and stabilization of the claspless denture will be carried out using wedge-shaped body of elastic material, the amount of which is calculated individually depending on the above parameters and fills the area between the denture and supporting teeth of the patient. The optimal ratio of undercut and height of the inclined teeth is discussed. When the mesio-distal tilt angle is more than 45°, there are difficulties with the insertion of the prosthesis, and when tilted less than 15° it can have problems with fixing. Allowed the thickness of the silicone compound is from 0.1 to 2.4 mm When the thickness of the layer of material above 3.0 mm are possible complications in the form of breaking on period of exploitation.