Two problems connected with the transient motion of an elastic body acted upon by a moving-point force are solved by an application of the dynamic Betti-Rayleigh reciprocal theorem. This theorem, which is the analogue of Green’s theorem for the scalar wave equation, permits the solution to be written as a single expression, irrespective of the value of the (constant) moving-force velocity
v
v
. In particular, the displacement field in an infinite elastic body, due to a transient-point body force moving, in a straight line, is given in a simple form. Next the surface motion of an elastic half-space acted upon by a transient pressure spot moving in a straight line is analyzed for a material for which Poisson’s ratio is one-fourth. The normal displacement is expressed in a simple manner, but the tangential displacement is quite complicated and is not fully expressible in terms of elementary functions. Singularities of the displacement fields are identified and discussed.