The finite element method is one of the most powerful tools for analyzing soil structure interaction problems. This is attributed to its wide applicability. The method has, however, a week point especially in wave propagation problems. As the area analyzed by the method is limited to be finite, artificial boundaries must be introduced into the model when the problem treats a widely extent area such as ground. And special boundary conditions must be taken into consideration for the artificial boundaries. The boundary conditions are summarized into three categories, first, the energy transmitting boundaty, second, the superposition boundary and finally, the viscous boundaty. In this study, the viscous boundary for axisymmetric systems subjected to non-axisymmetric load is proposed by virtue of the principle of the virtual work. The effectiveness of the boundary was examined and it was found that the proposed method gave good results.