SummaryThe 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.