The problem considered here is that of a torsional impulsive body force within a semi-infinite elastic solid. The surface of the solid is assumed to be either stress-free or rigidly clamped. The basic solution is found to be essentially the same as that for the surface loading of a half space previously considered by Eason [1]. The displacement is determined in terms of elementary functions for one particular type of body force, although using the results in [1] the solution can be obtained for other types of force. Some numerical results for the surface displacement of the stress-free solid are presented in graphical form.