A study is made of the generation of SH-type waves at the free surface of a layered anisotropic elastic medium due to an impulsive stress discontinuity moving with uniform velocity along the interface of the layered medium. The exact solution for the displacement function is obtained by the Laplace and Fourier transforms combined with the modified Cagniard method. The numerical results for an important special case at two different distances are shown graphically. The results of the present study are found to be in excellent agreement with those of isotropic elastic media.