The model of the axis-radiate infinite element is developed for simulation of the infinite layered foundation underlain by a rigid base. Within the infinite element, the coordinate and displacement of any point are expressed by those of the nodes located on the artificial boundary, and concise mapping functions can easily express the attenuation character of the displacement field. By coupling finite and infinite elements, the elastic recovery capacity and radiation damping of the infinite layered foundation are simulated. In the numerical calculation, the infinite element mesh is performed only on the artificial boundary. Compared to FEM, the present approach needs less nodes and elements, and shows good accuracy and efficiency.