A solution of a plane model problem on stress-strain state of an orthotropic semi-infinite plate is presented. The plate is supported by a set of periodically spaced rigid overlay elements. Localized zones of sub-fracture grow along the boundary between the plate and an overlay element from the vertex to the center. They may be simulated by the lines of discontinuity of tangent displacements. Dimensions of the zones of sub-fracture and contact stresses are obtained numerically.