A damping device for inserting into a housing of an impulse producing drill machine, for damping Shockwave reflexes from a drill string connected to the drilling machine, is distinguished in that a first damping piston (7) for direct or indirect action against the drill string and for applying a pressure in the direction of the drill string an a second damping piston (9) for applying pressure in the direction against the drill string against a fixed stop (11) arranged in the housing, wherein the first (7) and the second damping piston (9) are arranged to co-operate for joint damping action with a drill bushing or shank adapter in a certain relative position. The invention also concerns a drilling machine.