We consider the magnetohydrodynamic (MHD) flow which is laminar, steady and incompressible, of a viscous and electrically conducting fluid on the half plane (y >= 0). The boundary y = 0 is partly insulated and partly perfectly conducting. An external circuit is connected so that current enters the fluid at discontinuity points through external circuits and moves up on the plane. The flow is driven by the interaction of imposed electric currents and a uniform, transverse magnetic field applied perpendicular to the wall, y = 0. The MHD equations are coupled in terms of the velocity and the induced magnetic field. The boundary element method (BEM) is applied here by using a fundamental solution which enables treating the MHD equations in coupled form with general wall conditions. Constant elements are used for the discretization of the boundary y = 0 only since the boundary integral equation is restricted to this boundary due to the regularity conditions at infinity. The solution is presented for the values of the Hartmann number up to M = 700 in terms of equivelocity and induced magnetic field contours which show the well-known characteristics of the MHD flow. Also, the thickness of the parabolic boundary layer propagating in the field from the discontinuity points in the boundary conditions, is calculated. (c) 2008 Elsevier B.V. All rights reserved.