To facilitate control, by easily removing residual deformation after deforming a base isolation layer, and preventing generation of a large operation sound when deforming the base isolation layer of a base isolation structure by a strong wind.

This damper 3 has a piston 7 sliding in a case 6, and the case 6 has an inner cylinder 10 and an outer cylinder 20 sealed with fluid, and a storage chamber 13 is arranged in a part of the outer cylinder 10. The inside of the inner cylinder 10 is partitioned into a first chamber 11 and a second chamber 12 for passing a rod 8. A check valve 100 for allowing only a fluid flow to the first chamber 11 from the second chamber 12, is arranged in a flow passage 7A for communicating the first chamber 11 with the second chamber 12. A first flow passage 10A for communicating the first chamber 11 with the storage chamber 13, a second flow passage 10B for communicating the second chamber 12 with the storage chamber 13, and an orifice 10D for communicating the first chamber 11 with the storage chamber 13 in parallel to the first flow passage 10A are formed. A relief valve 101 for making fluid in the first chamber 11 flow to the storage camber 13 when fluid pressure in the first chamber 11 becomes a predetermined value or more, is arranged in the first flow passage 10A. A suction valve 102 for allowing only the fluid flow to the second chamber 12 from the storage chamber 13, is arranged in the second flow passage 10B.