A plurality of laminated rubber or rubber-like elastoplastic ring-configured pads vertically stacked and secured together to provide seismic damping for a building structure. The laminated pads include ring-like steel plates or solid disk-like steel plates to form one laminated stage of a multi-stage seismic damping device. A plurality of damping devices are used to support a vibratable mass on a building structure. The combination of stacked ring-configured elastoplastic pads and steel plates provides a damping device having a high lateral deformation capacity with a long period and high resistance to buckling. The damping device is suitable for protecting building structures having long natural periods, such as multi-storied buildings.