This hydraulic damping device comprises a cylinder for containing oil; a reservoir chamber R which is provided in the outer part of the cylinder and in which liquid accumulates; a piston provided so as to be axially movable within the cylinder and dividing the space within the cylinder into a first oil chamber and a second oil chamber, which contain oil; a baffle member provided as a separate element from the cylinder, the baffle member having a body which is provided in the reservoir chamber R, and also having a protrusion which protrudes from the body, the baffle member preventing the waving of the surface of oil in the reservoir chamber R; and a limiting section (first section to be held) provided to the baffle member and limiting the movement of the baffle member on both one side and the other side in the axial direction.