- This paper is concerned with the scattering of a time-harmonic electromagnetic (EM) plane wave by a fast and slow moving PEC circular cylinder under the framework of Einstein’s Special Relativity. By applying the Lorentz and EM field transformations to the scatterer co-moving frame of reference, the problem is mapped into a plane wave scattering from a stationary cylinder. By using the well known (stationary cylinder) exact and asymptotic solutions, we obtain the scattered EM field in this frame. These fields are than mapped back to the incident-field frame of reference in which the cylinder is moving. This procedure yields the exact and asymptotic scattered EM fields. We discuss several relativistic wave phenomena such as shifted shadow regions, velocity-dependent incident and reflection angles and velocity-dependent creeping waves to name a few. Finally we apply a low speed approximation to the wave potentials and discuss the corresponding wave phenomena.