A boundary layer solution for the flow of an electrically conducting fluid over a semi-infinite flat plate in the presence of a transverse magnetic field and taking into account the heat due to viscous dissipation and stress-work has been recently presented by Soudalgekar and Takhar. However, they omitted some of the terms in the equations. The full boundary layer equations governing this problem can be quickly and accurately solved using finite difference techniques. The analytical solution for the velocity at large distances down the plate is derived and the numerical results approach this solution. A series solution, valid at small distances, shows good agreement with the complete numerical solution. © 1979.