A fracture mechanics problem for a coating linked to the basis made of another elastic material is considered. It is assumed that in the vicinity of technological defect (crack) in the process of loading in the coating, there will arise prefracture zones (damages) that are modeled as the areas of weakened interparticle bonds of the material. In the prefracture zones (interlayers of the overstressed material), the coating material is deformed beyond the limit of elasticity. It is considered that during loading in the cross section of the coating in the vicinity of the crack, there is an arbitrary number of rectilinear prefracture zones. The condition determining the limiting value of the external load at which the crack growth happens is obtained.