A damper for damping the vibration or the like caused by an earthquake, comprising: at least a hollow outer elongated body and a hollow inner elongated body; said inner elongated body including an inserted portion which has an outer surface extending in an axial direction and disposed with a gap with respect to an axially extending inner surface of said outer elongated body, and which is inserted in said outer elongated body so as to be relatively movable in the axial direction, a viscous or viscoelastic body being disposed in the gap between the inner surface of said outer elongated body and the outer surface of said inner elongated body in such a manner as to be in contact with the inner surface and the outer surface, a one-side attaching plate member being secured to another end portion of said outer elongated body, and characterized in that one end portion of said inner elongated body integrally extends from said inserted portion in the axial direction and projects to the outside from one axial end portion of said outer elongated body, an other-side attaching plate member is secured to the one end portion of said inner elongated body, and said viscous or viscoelastic body, which is set in a hermetically-sealed state, is further filled in the interior of a hollow cylindrical portion (36, 38) of at least one of said outer and inner elongated bodies (21, 22), said damper further comprising a compressible body which is embedded in the viscous or viscoelastic body filled in the hollow cylindrical portion (36, 38) of at least one of said outer and said inner elongated bodies (21, 22), and whose volume decreases or increases due to the increase or decrease of the internal pressure of the viscous body or the viscoelastic body. at least a hollow outer elongated body and a hollow inner elongated body; said inner elongated body including an inserted portion which has an outer surface extending in an axial direction and disposed with a gap with respect to an axially extending inner surface of said outer elongated body, and which is inserted in said outer elongated body so as to be relatively movable in the axial direction, a viscous or viscoelastic body being disposed in the gap between the inner surface of said outer elongated body and the outer surface of said inner elongated body in such a manner as to be in contact with the inner surface and the outer surface, a one-side attaching plate member being secured to another end portion of said outer elongated body, and characterized in that one end portion of said inner elongated body integrally extends from said inserted portion in the axial direction and projects to the outside from one axial end portion of said outer elongated body, an other-side attaching plate member is secured to the one end portion of said inner elongated body, and said viscous or viscoelastic body, which is set in a hermetically-sealed state, is further filled in the interior of a hollow cylindrical portion (36, 38) of at least one of said outer and inner elongated bodies (21, 22), said damper further comprising a compressible body which is embedded in the viscous or viscoelastic body filled in the hollow cylindrical portion (36, 38) of at least one of said outer and said inner elongated bodies (21, 22), and whose volume decreases or increases due to the increase or decrease of the internal pressure of the viscous body or the viscoelastic body.