A numerical analysis was conducted for mercury and lithium MHD flows in rectangular channels under uniform transverse magnetic fields. In order to couple electromagnetic effects with hydrodynamics, the axial momentum equation and the equations for the axial induced magnetic field in the fluid and wall were solved simultaneously. The suppression of turbulence was taken into account by using the modified k - ε model of turbulence. The analytical results agreed well with the experimental results for the velocity profiles in mercury flow and skin friction coefficients in mercury and lithium flows. The M-shaped velocity profile for lithium flows was found, which is expected to be one reason for heat transfer enhancement at the wall parallel to the magnetic field.