This hydraulic damping device is provided with: a cylinder 10 for containing oil; a reservoir chamber R which is provided in the outer part of the cylinder 10 and in which liquid accumulates; a piston provided so as to be axially movable within the cylinder 10 and dividing the space within the cylinder 10 into a first oil chamber and a second oil chamber, which contain oil; a baffle member 60 provided as a separate element from the cylinder 10, the baffle member 60 having a body 61 which is provided in the reservoir chamber R, and also having a protrusion 621 which protrudes from the body 61, the baffle member 60 preventing the waving of the surface of oil in the reservoir chamber R; and a limiting section (first section 63 to be held) provided to the baffle member 60 and limiting the movement of the baffle member 60 on both one side and the other side in the axial direction.