An effective modification for a thin-layered element, originally proposed by Waas, for the far field is presented so as to account for the soil-structure interaction of an axisymmetric structure on soil layers subjected to an incident earthquake motion. The modified model has dashpots at an interface, namely the bedrock, between a soil layer and an underlying infinite far field. The model can treat the problem of radiation of waves into a downward far field, as well as a horizontal far field. Based on the present formulation, a disk on an elastic half space subjected to a vertically oscillating force is solved and the result shows a fairly good agreement with a theoretical solution. A further practical application to the earthquake response of a heavy tower shell shows the effectiveness of the present method for problems of structures on horizontal soil layers subjected to an incident earthquake motion travelling vertically. The results reveal large differences in the response of the tower between the original Waas formulation and the present one.