In the contribution the limits of the validity of classical linear elastic fracture mechanics are extended to problems connected with failure of composite structures. The work is focused mainly on the case of a crack touching the interface between two different materials, two different constituents. The approach suggested in the paper facilitates the answer to the question what is the influence of particle (in particulate composite) or layer (in laminates) on crack propagation through bimaterial interface. Different composite (bimaterial) structures are considered: layered composites and composites reinforced by particles. The presented approach follows the basic idea of linear elastic fracture mechanics, i.e. the validity of small scale yielding conditions is assumed, and has a phenomenological character.