We introduce a computationally efficient quasi-rigorous method for the analysis of corrugated planar waveguide structures. The method is based on rigorous diffraction theory of gratings. The computational efficiency is achieved by using Redheffer's star product and the so-called binary method for the involution of the transfer matrix. The developed method enables efficient rigorous analysis of corrugated waveguide structures without any limitations for the corrugation depth. Comparison with the thin-film stack method shows that the proposed method gives similar results for Bragg grating for the fundamental mode when the corrugations are shallow, but the results differ significantly when the corrugations are deep. Furthermore, the quasi-rigorous method also facilities the analysis of the coupling of light from the fundamental mode into the higher waveguide modes.