We consider the magnetohydrodynamic flow that is laminar and steady of a viscous, incompressible, and electrically conducting fluid in a semi-infinite duct under an externally applied magnetic field. The flow is driven by the current produced by a pressure gradient. The applied magnetic field is perpendicular to the semi-infinite walls that are kept at the same magnetic field value in magnitude but opposite in sign. The wall that connects the two semi-infinite walls is partly non-conducting and partly conducting (in the middle). A BEM solution was obtained using a fundamental solution that enables to treat the magnetohydrodynamic equations in coupled form with general wall conductivities. The inhomogeneity in the equations due to the pressure gradient was tackled, obtaining a particular solution, and the BEM was applied with a fundamental solution of coupled homogeneous convectiondiffusion type partial differential equations. Constant elements were used for the discretization of the boundaries (y ?=? 0, -a ? x ? a) and semi-infinite walls at x ?=? +/- a, by keeping them as finite since the boundary integral equations are restricted to these boundaries due to the regularity conditions as y ????8?. The solution is presented in terms of equivelocity and induced magnetic field contours for several values of Hartmann number (M), conducting length (l), and non-conducting wall conditions (k). The effect of the parameters on the solution is studied. Flow rates are also calculated for these values of parameters. Copyright (C) 2011 John Wiley & Sons, Ltd.