The purpose of this paper is to study how the stiffness and weights of the support structure influence the response of the large span dome with seismic isolation system, when it's subjected to horizontal earthquakes. This system is applied to a latticed dome with about 300m span, and dynamic response analyses with various conditions are carried out to make it clear. From the results of the numerical studies, it is confirmed that the seismic isolation system with hysteresis dampers can almost reduce the vertical and horizontal acceleration responses of the dome, independent of the stiffness and weights of the support structure.