It is shown that simple elastic media in motion exhibit new properties, owing to the effective compressional and shear wave velocities produced by the motion. Presently, we consider scattering of a compressional plane wave by (1) a half‐space moving parallel to the interface and (2) a cylinder moving along its axis. In both cases the assumed boundary conditions correspond to good contact at the interface. Computational results are given for the scattering amplitudes as a function of velocity and angle of incidence.