A system for damping seismic motions transmitted from a foundation to an architectural structure is disclosed. The system may include a stacked formation of elements including a washer, a sliding plate, and a damping member. The sliding plate may be fixedly connected to a base member of the architectural structure. During seismic motions, the washer may slide over the top of the sliding plate and the damping member may elastically deform. Accordingly, movement of the base member may trail movement of the foundation, and the acceleration experienced by the architectural structure may be reduced. A method of installing such a seismic damping system is also disclosed.