The problem of optimization of the elastic parameters values and the shape of one of the elements of the splinting arc prosthesis is considered. This denture is used in orthopedic dentistry to restore the dentition. Its optimized element is a soft lining between the basis of the prosthesis and the underlying mucosa, designed to reduce the negative influence of the masticatory load on the tissues of the prosthetic bed. The paper is focused on the problem of determining the material distribution of the backing layer, which would minimize the negative influence of the masticatory load on the underlying tissues. Methods of mathematical modelling are used. It is proposed to describe the distribution of the material of the backing layer with the help of a scalar function whose values determine its thickness at the corresponding point. The desired function is defined as the limit of a special functional sequence, on the elements of which the values of a number of criteria are successively reduced. The applicability of the proposed approach is illustrated on a simplified model example, which is based on a two-dimensional inhomogeneous elasticity problem. The results of numerical modelling are presented.