Integrals representing the reflected and diffracted elastic waves generated by the incidence of a plane compressional wave on a rigid quarter-plane are evaluated by an application of the Cagniard-De Hoop technique. It is shown that diffracted spherical waves radiate away from the tip of the quarter-plane at the shear and compressional wave speeds. The spherically spreading compressional wave excites secondary shear waves on the surfaces and edges of the quarter-plane. These secondary spherical wavelets envelope a ruled surface which is conical in shape at the edges of the scatterer. The envelope propagates away from the quarter-plane at the critical angle and forms a Mach wave or bow wave. The usual reflected shear and compressional plane waves are also present and combine with the diffracted waves to form the geometric shadow of the quarter-plane.