Abstract A mathematical model for fluid catalytic cracking units is developed. The model takes into account the kinetics of the cracking reactions, as well as the kinetics of coke combustion in the regenerator. A numerical scheme is developed for the solution of the model equations. It is found that multiplicity of the steady states extends over a wide scope of operating variables and parameters. The model investigates the effects of catalyst circulation rate and gas oil flow rate, which have a strong effect on the reactor temperature and hence yield and selectivity. The phenomenon of hysteresis has been investigated. The model can be used for yield optimization and steady state control.