Abstract <p>The problem of estimating the strength of a composite plate made of a brittle material with a longitudinal shear crack is considered. Regular every where solutions of fracture mechanics, which are constructed as generalized solutions depending on a scale parameter, are used. These solutions are found as the solutions of inhomogeneous Helmholtz equations with a singular classical solution of crack mechanics. It is shown that the dependence of the theoretically determined stress concentration on the scale parameter has a property of near-stationarity for the constructed generalized solutions and their combinations corresponding to strength criteria. This invariance property is used to construct a solution for the case of a mode II crack in a composite domain. For a composite material with a mode II crack, the properties of a master curve, the dependence of the stress intensity factor on the polar angle at the crack tip, and possible fracture features are discussed with allowance for the fact that the scale parameter in the theory of regular cracks is an additional physical characteristic of the microstructure of a material.</p>