The new multistage-type H2/H2O exchange column using hydrophobic catalysts without the superheating section, which separates the water/vapor scrubbing step and the vapor/hydrogen exchange step, is one of the most attractive processes for hydrogen isotope separation. The present study deals with two exchange columns of this type that seem to be feasible. One is a column processing D2, D2O, HD, HDO, DT, and DTO, which is a unit process for recovery of tritium and removal of protium from the heavy water used as the moderator for nuclear fission reactors. The other is a column processing H2, H2O, HD, HDO, HT, and HTO for a decrease in volume of the tritiated water produced by the operation of tritium facilities. A mathematical simulation procedure is developed for these columns. The rigorous solutions of all the basic equations derived from requirements for conservation of material and phase equilibrium on any stage are effectively found out by means of a successive iteration method. This method uses the tridiagonal matrix algorithm, which is often used in distillation calculations, modifying it to make it applicable to the cases where three phases (liquid water/water vapor/hydrogen gas) must be considered. It is also shown that a specific convergence technique is needed to accelerate the progress of the iterative calculation or to ensure achievement of convergence. Several numerical experiments indicate that this simulation procedure is applicable in a fairly wide range of calculational conditions.