A damping device has a liquid vessel into which a liquid is injected having a wave motion water surface such that the wave motion direction of the wave motion of the water surface is in the elongated direction of the vessel. Damping members are provided in order to damp the sloshing of liquid in the liquid vessel, and wave dissipation devices are disposed at a portion not always soaked in liquid in the liquid vessel. Accordingly, the vibration of a construction occurring by wind, earthquake and the like is absorbed by the viscosity resistance occurring between the liquid and the damping members, and the vibration is restricted. Moreover, damping performance can be efficiently exercised by providing various installation arrangements.