A damper for damping the vibration of a building 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, and one end portion which 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; a viscous body or a viscoelastic body, which is set in a hermetically sealed state, 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, an other-side attaching plate member being secured to the one end portion of said inner elongated body; characterized in that said damper further comprises a flexible partition wall for partitioning a hollow portion of at least one of the inner elongated body and the outer elongated body into a chamber with the viscous body or viscoelastic body filled therein and an air chamber, and for increasing or decreasing the volume of the chamber by the increase or decrease of the internal pressure of the viscous body or viscoelastic body based on the extension or retraction of the inserted portion of the inner elongated body in the axial direction with respect to the interior of the outer elongated 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, and one end portion which 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; a viscous body or a viscoelastic body, which is set in a hermetically sealed state, 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, an other-side attaching plate member being secured to the one end portion of said inner elongated body; characterized in that said damper further comprises a flexible partition wall for partitioning a hollow portion of at least one of the inner elongated body and the outer elongated body into a chamber with the viscous body or viscoelastic body filled therein and an air chamber, and for increasing or decreasing the volume of the chamber by the increase or decrease of the internal pressure of the viscous body or viscoelastic body based on the extension or retraction of the inserted portion of the inner elongated body in the axial direction with respect to the interior of the outer elongated body.