The general character of the magnetohydrodynamic flow past a non-conducting flat plate in the presence of transverse magnetic fields is analysed in some detail. The appropriate extension of the Rayleigh problem to the magnetohydrodynamic case is shown to yield solutions which correctly predict some features of the steady flow past a semi-infinite flat plate; in addition, it is shown that the knowledge of these significant features permits an easy evaluation of their magnitudes in other extensions of the Rayleigh problem. The flow past a semi-infinite flat plate is analysed by two methods. First, by linearizing the governing equations and incorporating the assumption of a low ratio of viscous to magnetic diffusivity, the results for skin friction and the normal component of magnetic field at the plate are obtained and are shown to be useful in interpreting the character of these low conductivity flows. Secondly, the complete set of governing equations is formulated as a finite difference problem and solved numerically on a digital computer. The results obtained, in addition to demonstrating feasibility of the numerical calculations, show that the disturbance produced by the plate is no longer confined to a thin viscous layer if the ratio of viscous to magnetic diffusivity is greater than 10−2, but that an appreciable Alfvén type disturbance is excited.