Herschel-Bulkley model is used to describe rheological behavior of the Magnetorheological (MR) fluids subject to an applied magnetic field. Based on momentum equation, the effect of the applied magnetic field on the pressure driven flow of the MR fluids in the cylindrical pipe is analyzed theoretically. The expressions for the velocity and the volumetric flow rate in viscoplastic flow are derived to provide a theoretical foundation for the design of cylindrical pipe MR devices. The results indicate the MR fluids have the properties of both viscosity and viscoplasticity. The flow of the MR fluids in the cylindrical pipe exhibits viscoplastic flow behavior. The velocity exhibits the distributions of both parabolic curve and straight line with the magnetic field direction. The volumetric flow rate can be continuously adjusted by an external magnetic field.