Magnetorheological fluid (MR fluid) is highly concentrated suspension of very small magnetic particle in inorganic oil. The essential behavior of MR fluid is its ability to reversibly change from free-flowing, linear viscous liquids to semi-solids having controllable yield strength in milliseconds when exposed to magnetic field. This feature provides simple, quiet, rapid-response interfaces between electronic controls and mechanical systems. In this paper, a mini-bus MR fluid damper based on plate Poiseuille flow mode is typically analyzed using Herschel-Bulkley model, which can be used to account for post-yield shear thinning or thickening under the quasi-steady flow condition. In the light of various value of flow behavior index, the influences of post-yield shear thinning or thickening on flow velocity profiles of MR fluid in annular damping orifice are examined numerically. Analytical damping coefficient predictions also are compared via the nonlinear Bingham plastic model and Herschel-Bulkley constitutive model. A MR fluid damper, which is designed and fabricated according to design method presented in this paper, has tested by electro-hydraulic servo vibrator and its control system in National Center for Test and Supervision of Coach Quality. The experimental results reveal that the analysis methodology and design theory are reasonable and MR fluid damper can be designed according to the design methodology.