Summary: We show that finite element methods can be used for determining the flow in a straight channel under a variety of wall conductivity conditions when a uniform magnetic field is imposed perpendicular to flow direction. At high Hartmann numbers oscillatory solutions are found unless sufficient points are placed within Hartmann layers. In some one- and two-dimensional problems it appears that it is adequate to place one or two points within the Hartmann layer to remove the oscillations. Central core values can sometimes be predicted with good accuracy, even when the Hartmann layers are not resolved adequately. A nine-point Gauss point rule has been used to evaluate the stiffness and other matrices for eight-node elements.