Extension of Rayleigh's problem to magnetohydrodynamics is investigated for a perfectly conducting plate with a transversely applied magnetic field. Induced electric and magnetic fields are both included in the analysis. Results obtained show that along the plate an electromagnetic body force will actinthe direction of fluid motion. The results are found to be the same whether the applied magnetic field is fixed‐in‐space or attached to the moving plate. A comparison of these results with those of Rossow (magnetic field fixed with fluid) shows opposite trends in the velocity profile. Such discrepancies are discussed. Rossow's second case (magnetic field fixed with plate) is also discussed.