Problems of interaction of electromagnetic waves with plane screens situated in moving nondispersive medium and in moving cold plasma are considered. It is assumed that the medium is able to move both along the screen and through it (in this case, the screen was assumed to be permeable to particles of the medium). The main attention is focused on a scattering of point sources' fields by a conductive plane and on the diffraction of plane waves by the half-plane and by a slot. The basic physical effects differing radically from the effects that occur in a stationary medium are described. In additional, the averaged boundary conditions for periodic structures of parallel conductors in the above mentioned moving media and some stationary media are given as well.