Summary: Treated are line loads travelling with constant speed on the surface of an inhomogeneous elastic half space, the materials considered being such that uncoupled motions can arise. Assuming a quasi static state, solutions are presented for (i) a line force in the plane of the surface, acting in a direction perpendicular to that of its motion (called SH line load), and (ii) a normal line force moving in a direction perpendicular to its length.