A damping device, particularly for damping or avoiding pressure surges such as pulses, in hydraulic supply circuits, preferably in the form of a silencer, includes a damping housing that surrounds a damping chamber (19), has at least one fluid inlet (11), has at least one fluid outlet (13) and has a fluid receiving chamber (19) extending between the fluid inlet (11) and the fluid outlet (13). During operation of the device, a fluid flow crosses the damping chamber (19) in a through-flow direction (15), coming from the fluid inlet (11) in the direction of the fluid outlet (13). At least parts of the fluid receiving chamber (19) extend in at least one extension direction transversely with respect to the through-flow direction (15). The fluid receiving chamber (19) immediately adjoins the fluid inlet (11) and the fluid outlet (13) and is delimited by at least one yielding wall part (4).