A hydraulic damping device is provided having a rubber elastic body, a rubber film member closing an opening of the rubber elastic body so as to define a closed chamber, and a partition member dividing the closed chamber into two liquid chambers. A restricted liquid passageway interconnects the two liquid chambers. A cylindrical frame member composed of a resin material having a low coefficient of thermal conductivity is joined to the outer peripheral surface of the rubber elastic body. A support member composed of an aluminum alloy is secured to the outer peripheral surface of the frame member and is connected to an engine. When the support member receives a large amount of heat from the engine, the rubber elastic body is thermally insulated from the support member by virtue of the resin frame member, and accordingly, can be prevented from deteriorating due to the heat of the engine. In addition, by composing the support member of an aluminum alloy, the weight of the device can be reduced.