One of the most important parts in the development of generation IV nuclear reactors is safety. In the research on generation IV sodium-cooled fast reactors, magnetohydrodynamic (MHD) circulators have received attention for the stable transport of coolants. In this study, the stability of an MHD circulator was evaluated using a mathematical approach to obtain the critical value of the developed pressure. The critical developed pressure equation is a function of the flow rate and dimensionless parameters, which were derived from the theoretical model of the MHD circulator with a dimensionless scaled velocity, flow rate, and pressure. The stability conditions expressed using the critical value of the developed pressure and dimensionless parameters were investigated according to the changes in the main design variables of the MHD circulator. The relationships between the dimensionless parameters, stability, and main design variables constituting the stability boundary of the MHD circulator were analysed. The stability of the MHD circulator is considered safe when the stability criterion epsilon is lower than 1. The geometrical variables such as the duct thickness or width of the flow gap and electrical variables such as the frequency were the main parameters affecting the flow stability in the MHD circulator.