In this thesis, a method for solving soil-structure interaction problems of structures on semi-infinite elastic media is studied. It is based on a combined usage of the conventional finite elements for the nearfield and the newly developed infinite elements for the far field. The key to success of the method is the proper definition of the shape function of the infinite element. Based on Gauss-Laguare quadrature, the characteristic matrices of the infinite element are computed for the static as well as the dynamic axisymmetric elements. Verification of the method has been carried out on a rigid circular plate on a semi-infinite elastic half space. Numerical analysis have been performed for a containment structure of a nuclear power plant for seismic excitations.