The paper deals with the propagation of shear horizontal (SH) waves in an nonhomogeneous elastic half-space composed of a layer whose shear modulus and mass density have a power dependence on the distance from the lower plane and the periodically stratified half-space. The equation which relates the wave speed to the wave-number and functions of the shear modulus and mass density is derived. The wave velocity is analyzed numerically. Especially, the influence of mechanical properties of the coating layer and the stratified foundation on the wave velocity is presented in the form of figures.