High-speed flows over a backward-facing step that is subject to an applied magnetic field are numerically simulated. The global domain of computation has been decomposed into upstream and downstream domains from the step location. The low magnetic Reynolds number approximation under a multiblock grid approach is used for modeling the backstep flow. Flux-vector splitting for the convective terms and central differencing for the diffusion terms are used. A time-explicit multistage Runge-Kutta scheme for time integration is implemented. Pressure distribution for the Navier-Stokes analysis is found to be in good agreement with the experimental data. Different types of magnetic field distributions are investigated. Both uniform and variable electrical conductivity distributions have been considered. It has been observed that an increase in the separation zone and displacement of oblique shock wave toward the exit section occurs subsequent to application of the magnetic field. Comparison of results obtained with uniform and variable electrical conductivities has shown a reduction in magnetic interaction for variable electrical conductivity. Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.