This paper attempts to explain MHD instabilities observed in aluminium reduction cells. The model analysed is a plane horizontal poorly conducting fluid layer, sandwiched between two highly conducting semi-infinite layers, the lower one a fluid and the upper solid. A uniform normal current passes through all three layers, and the stability of small perturbations to the fluid–fluid interface is analysed. Plane waves are described which can be of either constant or exponentially growing amplitude, depending on the form of the magnetic field due to distant current sources. A model of an electric are furnace in which the upper layer too is fluid is considered, and in this case MHD effects can also be destabilizing.