This paper presents a two-dimensional Computational Fluid Dynamics (CFDs) simulation for the steady, laminar flow of an incompressible magnetorheological (MR) fluid between two fixed parallel plates in the presence of a uniform magnetic field. The purpose of this study is to develop a numerical tool that is able to simulate MR fluids flow in valve mode and determine B-0, applied magnetic field effect on flow velocities and pressure distributions. A uniform transverse external magnetic field is applied perpendicular to the flow direction. The equations governing the steady flow of an incompressible MR fluid are implemented in the commercial code Ansys 14.0 Fluent which is a flexible CFD code based on finite volume approach. The governing differential equations describing the flow between parallel plates under magnetic field are solved numerically by using Fluent MHD module based on solving the magnetic induction equation method. The external applied magnetic field, B-0, takes values between 0 and 1.5 T with 0.5 T step size, was applied to determine B-0 effects on fluid flow. The numerical solutions for velocity and pressure distributions were obtained for different magnetic fields. It was observed that increase in B-0 leads to decrease flow velocity. Results, obtained from numerical study was plotted graphically and disgusted in the present paper. Crown Copyright (C) 2012 Published by Elsevier Ltd. All rights reserved.