A theoretical model to study the performance characteristics of a magnetohydrodynamic (MHD) power plant is presented. The model takes into account the external and internal irreversibilities. General expressions for power and efficiency of the power plant are derived when the MHD generator is operating at constant velocity and constant Mach number conditions. It is shown that when the generator and compressor are running reversibly, the constant velocity and constant Mach number cases are identical in performance and the efficiency at maximum power is identical to Curzon-Ahlborn efficiency. It is also shown that the constant velocity case produces less entropy generation in the generator than that of the constant Mach number case when the generator electrical efficiency is less than one. Copyright (C) 2000 John Wiley & Sons, Ltd.