Recently, Magneto-Rheological (MR) dampers attract a great deal of attentions from many researchers as the semi-active control devices. In the MR damper, a MR fluid is used. The properties of the MR fluid can be controlled in accordance with the magnetic field. Therefore, the force generated by the MR damper is adjustable by changing the magnetic field at the orifice of the damper. In this paper, the force-velocity relationship of the MR damper is analytically studied. Based on the fluid dynamics with the Bingham model and Herschel-Bulkley exact relationships between piston velocity and generated force are obtained. It is confimed that each analytical result can predict the behavior of the MR damper exactly.