An exact relativistic solution to the problem of electromagnetic wave scattering by uniformly translating bodies can be performed by applying Lorentz field transforming formulae to plane wave spectra representing impinging and scattered fields. An application to the two-dimensional problem of a monochromatic plane wave scattering for the case of one cylinder in the presence of a plane interface has been carried out. By virtue of a peculiar notation for electromagnetic vector fields used throughout the paper, the application of Lorentz formulae to plane waves and to plane-wave expandable fields can be easily expressed by altering propagation parameters (amplitude, frequency and direction).