A reservoir comprises an upper reservoir part and a lower reservoir part divided by a member into a first reservoir chamber and second reservoir chamber. The reservoir mounts to a shock absorber having a generally cylindrical body. At least the lower reservoir part is delimited by two parallel-displaced flat base surfaces and has a reservoir wall as a contacting surface between these base surfaces. The reservoir has a vertical extent that is substantially parallel with the shock absorber body. One of or both of the base surfaces of the lower reservoir part are kidney-shaped and are connected by the reservoir wall so that the lower pat of the reservoir has a vertical extent that partially follows the cylindrical shape of the shock absorber body