A thorough analysis of the fracture behaviour of a bimaterial plate, with a crack in one of its constituent materials and arbitrarily oriented with respect to the interface, was undertaken. The loading of the plate consisted of a uniform compressive or tensile stress applied along the crack surfaces. The influence of the crack position and orientation with respect to the bimaterial interface, as well as the elastic constants of the materials of the composite plate, on the critical stress required extension from the appropriate crack tip and the crack extension angle was studied. The characteristic cases of a single cracked plate with a stress-free and a rigid boundary, as well as the bimaterial plate with various material combinations of its constituents, were analysed. From the whole study interesting results were derived.