The interaction of an obliquely incident plane monochromatic EMW with a dielectric slab moving parallel to its boundaries and with a dielectric cylinder moving in the axial direction is considered. The moving dielectric media have an arbitrary velocity profile. The reflection coefficient and the backscattering cross section are determined for the cases of the one-dimensional (plane) and two-dimensional (cylindrical) geometries respectively. The special case of a parabolic velocity profile is numerically considered by the multi-layer technique using Maxwell's equations and MinkowBki's constitutive relations for moving media. Resonant phenomena have been noticed in the one-dimensional plane stratified medium for the large values of electric thickness of the slab.