The electromagnetic diffraction by two parallel plates of semi-infinite length is treated by ray methods. Two special problems are considered: (i) calculation of the fields in the forward and backward directions due to diffraction of a normally incident plane wave by two nonstaggered parallel plates; (ii) calculation of the field due to a line source in the presence of two staggered parallel plates when the source, the two edges, and the observation point are on a straight line. The crucial step in the ray-optical analysis is the calculation of the interaction between the plates. This calculation is performed by two methods, namely, the uniform asymptotic theory of edge diffraction and the method of modified diffraction coefficient. The relative merits of the two methods are discussed. The ray-optical solution of problem (i) agrees with the asymptotic expansion (plate separation large compared to wavelength) of the exact solution.