The paper is devoted to an applied problem of elastic shape optimization. This problem appears in prosthetic dentistry and consists in finding an optimal shape of ceramic restoration (microprosthesis) for reconstruction of a pulpless tooth without reinforcing posts. It is supposed that the optimal shape of the prosthesis is that provides the uniform distribution of stress values at the ceramic restoration boundary with the tooth tissues under a given external static loading. An admissible shape of microprosthesis must satisfy size, isoperimetric and other constraints that are natural for this problem. The main goal of the study is development of approaches to finding the microprosthesis shape that is close to the optimal one (suboptimal shape). The methods of mathematical and numerical modelling are used. The mathematical model of the problem is developed under assumption of homogeneity and isotropy of material of the inhomogeneous construction “tooth-prosthesis”. To find the suboptimal shape, the sequential approximation method is applied. The admissible initial shape of the contact boundary is specified. Then, a sequence of shapes is constructed, where each subsequent shape is obtained from the previous one by means of a special local variation of the contact boundary. This variation provides fulfilment of all restrictions on the shape and reduces the value of optimized functional of each subsequent shape. As a result, a close to optimal shape of the contact boundary is constructed. The applicability of the suggested approach is illustrated with the case of simplified two-dimensional statement of the inhomogeneous elastic problem. The solution of this problem describes the stress-strain state of the inhomogeneous structure in its particular plane section. Such a simplified statement occurs as a result of using the well-known method of plane sections. Results of mathematical modelling and numerical simulations are presented.