Beam-to-column connections with a wedge device show linear-from-origin-type restoring force characteristics and can possess self-centering capability that reduces residual horizontal displacements of a structure acted by an earthquake force. The connection with the wedge device can be used at an outer column, but it can hardly to be applied to an inner column. An numerical- analytical study on frame with wedge-device beam-to-column connection was carried out to clarify deformation behavior of the multi-story structure. The analysis results showed that the reduced residual horizontal displacement was after the ground motion.