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. Thin-walled structures are widely used in various fields in modern technologies of mechanical engineering, construction, aviation industry, shipbuilding, rocket engineering, oil, gas and other industries. Variety of forms of such structures, various loading conditions and pinning, presence of defects and inhomogeneities lead to wide range of different formulations of the problems of research on strength characteristics of such structures and methods used for this purpose. Literature review. The characteristic feature of this type of problems is the difficulty of solving them both using analytical methods and numerical calculations on computer. Therefore, the study of this problem is still relevant. Intensive search continues both in theoretical study of the problem and in development of approximate numerical calculation methods. Study on the convergence of the numerical method is of great importance in the development of numerical methods for solving practical problems using the finite element method. It is very important to have an opportunity to explore the validity of numerical method by comparing it with analytical solution of such a problem. Among the first studies in this area there are works of V.Z. Vlasov, G.Yu. Dzhanelidze, Ya.G. Panovko, S.N. Kan, E. Reissner. Tasks for composite shell structures in accordance with their actual interaction were solved by V.I. Mossakovskiy and his students using method of homogeneous solutions. Application of direction with functions having non-integrable singularity developed by G.Ya. Popov [1] and his students allowed to solve many problems for mechanics of deformable solids including problems for shell structures. The authors of this article developed a method that allowed to solve effectively the problem of stress state of lamellar shells [2]. Application of this method with the method of regularization of divergent integrals [1] allowed to solve a number of problems for the lamellar shells with defects, such as [3...6]. Aim of the Research is to solve the problem of plane-bending stress state of box shell with rectangular profile and infinite length under the indentation of two symmetrically arranged thin rigid inclusions. Main Body. Let’s consider the problem of stress state of box shell with infinite length and rectangular profile under the indentation of two thin rigid inclusions symmetrically located on the opposite faces (Fig. 1). The load acting on shell will be assumed symmetrical about the plane of symmetry of the shell. Let’s use the method of calculating the box shells [2], retaining the notations. The problem reduces to finding the solution of differential equations system y Р

Stress state of the box shell under the indentation of two inclusions