A study is made of stresses and displacements induced in an elastic half plane (plane strain) by a concentrated line load moving at a constant speed along its surface. The stress field for an arbitrary load distribution can be built up by superposition of these concentrated-load solutions. Three cases are considered: (a) The load is moving more slowly than either the longitudinal or transversal wave speeds of the elastic medium (subsonic case). (b) The load speed is between the two wave speeds (transonic case). (c) The load speed is greater than either wave speed (supersonic case). In each of these cases the nature of the singularity caused by the load is examined and the complete solution is given.