AbstractA study is made of the generation and propagation of transient wave motions in a layered elastic medium due to an asymmetric discontinuity of shear stress acting over a finite circular region at the interface of the composite medium. The problem is solved by the joint Laplace and Hankel transforms combined with Cagniard's method for exact evaluation of the integral solution. SurfaceP‐ andSV‐ wave motions are obtained in closed form assuming both dilatational and shear wave velocities are equal in the top finite layer and in the half space. On the other hand,SH‐wave motion for the general case is expressed in a series, each term of which is evaluated exactly by Cagniard's method. It is shown that the solution is oscillatory in nature and the number of oscillations increases with increasing asymmetry and decreasing ratio of the thickness of the upper layer to the radius of the circular region of the applied stress distribution. Some numerical calculation is carried out to investigate the nature of the displacement field as well as the reflected pulses. Numerical results are graphically presented in three dia