The Cagniard-de Hoop method is used to investigate elastic-wave tunneling through a thin high-velocity layer. The results indicate high-frequency attenuation in the geometric shadow zone. Attenuation is roughly proportional to layer thickness. Comparison of results obtained by omitting the high-velocity layer but using an average Q operator shows that effects of the high-velocity layer are similar to Q effects, with the equivalent Q for a given layer thickness varying as a function of source-receiver distance. These attenuation effects are explained in terms of deformation of the de Hoop contour.