In this paper we consider a problem of the response of an elastic half space subjected to an antiplane shear load. The load is suddenly applied and thereafter moves in an interval reciprocally as a trigonometric function of time. An analytical solution for the displacement is obtained in terms of single integration. It is shown that the discontinuity in the displacement occurs only for the case that the initial (maximum) speed of the load is greater than the speed of SH-wave. In this case the displacement has a finite jump on the leading wave front and a logarithmic discontinuity immediately behind the wave front which emanates from a point where the load speed comes up with SH-wave speed. Numerical calculations are carried out for several cases of the initial (maximum) speed of the load and are shown graphically.

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