The diffraction of an electromagnetic plane wave by a perfectly conducting semiinfinite plate is considered. The magnetic field of the wave is parallel to the edge of the plate. An analytic solution of the problem is found in the form of two overlapping expansions in positive and negative powers of the plate thickness. As an example of the use of the solution obtained, the asymptotic behavior of the reflection coefficient at the open end of a thick-walled waveguide is described. Numerical results given by the asymptotic equations are compared with the results of a rigorous calculation.