The paper deals with the theory of the propagation of microwaves, passing from a homogeneous and isotropic medium into a set of parallel metallic plates. The plane of separation between the set of plates and the homogeneous medium outside is assumed perpendicular to the plates. The incident wave is plane, and its direction of propagation is in the plane containing the perpendiculars to the plates and to the surface of separation. The electric field is parallel to the plates.The method is relatively simple. The study is based on Maxwell's equations and on periodicity and continuity considerations. An analytic method is introduced for the solution of the infinite set of linear equations with an infinity of unknowns, which arises from the continuity conditions at the boundary plane of the plate edges.Formulae are obtained giving the nature, direction, phase and amplitude of the reflected and transmitted waves. The reflected waves follow the usual laws found in the grating theory. In the case when only one non-evanescent plane wave is reflected, the transmission and reflection power coefficients are those obtained at the junction of two semi-infinite transmission lines corresponding to the free-space and the plate medium respectively. The analogy with transmission lines is more complex when two non-evanescent waves are reflected. For the usual angles of incidence and plate spacings the transmission power coefficient is high (maximum 99.5%), and the phase shift on transmission is small.