On a multi-layered base described by the Lamé equations there is a defective coating in the form of Kirchhoff plates. Defects of two types divide the covering into two half-planes with parallel ends, which, in the first case, are spaced apart from each other by a finite distance, and in the second case the distance is absent. All types of contact of coatings with a base are studied: in the absence of friction, in the presence of shearing stresses, with complete cohesion of the coatings and the base. The stress concentration in the end zone is investigated. The block-element method is used, which allows for studying the boundary problems mathematically. A complete analysis of the stress concentration features in the problem is performed.