This paper considers the fracture problem of a composite which consists of perfectly bonded parallel load-carrying laminates and buffer strips. It is assumed that both materials are isotropic and linearly elastic and also that the fatigue cracks may appear and spread in main laminates or in buffer strips or in both perpendicular to the interfaces. The external load is applied parallel to the crack surfaces and away from the crack region. The problem is solved for fully embedded cracks and for completely broken laminates or buffer strips. The mixed boundary conditions of the problem lead the analysis to a system of two singular integral equations for the crack surface displacement derivatives. These integral equations are solved numerically and mode III stress intensity factors are calculated.