Propagation of elastic waves from thicker to a shallower infinite layer is an important phenomenon in engineering, for instance in the earthquake engineering, as the variation of the dimension of the layer has considerable impact on the intensity and the distribution of the wave motion. The paper presents the computing procedure for wave motion field in both layers when the motion is excited by a given displacements in the thicker layer. Modeling of the layers is by FE and the Computation is in the frequency domain. The radiation conditions are considered exactly by considering all propagating wave modes in the layer and so the procedure yields exact results within the accuracy of the FE modeling. Theoretical basis of the analysis is briefly presented. The presented numerical examples are for the case of 2D anti-plane shear wave motion of some simple cases, although the presented procedure is applicable to non-homogeneous layers as well. The results of the analysis are briefly discussed.