The development of a new algorithm for steady-state modeling of multistage three-phase separation columns is presented. In the developed algorithm, prior knowledge of phase pattern in the column is not required. The phase pattern determination and equilibrium calculations are carried out simultaneously. The stability of a phase is determined by coupling a stability equation with the model equations of the column. The resulting nonlinear model equations of the system are solved using an "inside-out" method. The ability and flexibility of the algorithm for the simulation of three-phase separation columns are shown by solving a variety of three-phase distillation column examples. The algorithm is also applicable to two-phase separation columns.