The diffraction of transient elastic waves by a spherical cavity is treated. Two cases are considered: (1) A suddenly applied normal point load, and (2) the impingement of a plane transient dilatational pulse on the cavity. The method used determines the solution only in the shadow zones; that is, those points which cannot be connected to the source of disturbance by straight-line rays. Analytical results are obtained and evaluated for the displacements at the cavity wall.