Exact expressions are obtained for the displacement field in a homogeneous isotropic elastic half space whose surface is subjected to a unit normal pressure. The load emanates from a point and expands nonuniformly and radially outwards. The displacement field is obtained in the form of triple integrals over finite ranges. Both accelerating and decelerating loads have been considered. Wave front surfaces with their regions of existence have been identified. First motion approximations near different wave arrivals have been obtained by a limiting process and do not involve any integration. © 1979.