In engineering practice many constructions, buildings, or their parts contain stress concentrators such as cracks (cuts, slits), inclusions, patches, holes and angle points because of the conditions of production. During the exploitation of different constructions and their details, some of these concentrators can appear. Therefore, the analysis of stress state of massive bodies, containing the stress concentrators, and local stress fields, originated next to the concentrators, is the actual problem from the scientific and engineering points of view.In the present monograph, the problems of simultaneous interaction of different types of the stress concentrators with the massive deformable bodies are investigated. Many new contact and mixed problems are researched, the closed solutions are defined and the behavior of interaction of different concentrators is revealed. The solutions of non-standard mixed boundary value problems for plane and half-plane are obtained by the method of discrete singularities and orthogonal polynomials.