It is very important to estimate the contact stresses in the elastic materials with parallel and cross inclusions because it has applications in building, engineering, electronics, mine engineering. Traditionally the studies are carried out for an individual fixture, and then found parameters are accepted for all other facilities. At the same time a plurality of such facilities may lead to the occurrence of another factor badly affecting the strength. This factor is connected with the capability to localize the state of strain in one of the structure's zones, which results an exceeding of the planned strength parameters. The calculating theory of strength properties of these objects in the present scientific work is based on the example of the underground structures. The investigation use the block element method, which is based on the factorization approaches. The problem comes to the Fredholm's system of the integral equations of the second kind. It is succeeded to turn integral equation to the system of the algebraic equations, which are accessible to the analytical analysis, allowing finding out the strain and shift by means of the calculation of the integrals, describing the kernels of these equations by the theory of residue. The algorithm of realizing this investigation is presented. The possibility of the factorization methods for the such problems are discussed.

В основе исследования лежит метод блочного элемента, опирающийся на факторизационные подходы. Проблема сводится к исследованию системы интегральных уравнений первого рода с разностным ядром, которая приводится к системе интегральных уравнений Фредгольма второго рода. Путем вычисления интегралов, описывающих ядра этих уравнений по теории вычетов, удается свести интегральные уравнения к системе алгебраических, доступных для аналитического анализа, позволяющего выявлять напряжения или перемещения. Изложен алгоритм реализации подхода, обсуждаются возможности факторизационных методов в подобных задачах.