Steady state and dynamic simulation studies of the ITER Hydrogen Isotope Separation System (ISS) are presented. Ontario Hydro's FLOSHEET code has been used as the reference code for design studies of the ISS. Dynamic simulations were also carried out using Ontario Hydro's new DYNSIM code. Both codes have been verified against experimental and operating data from operating distillation systems. The DYNSIM code was used to model closed-loop control of the ISS under start-up conditions. The ITER ISS is expected to almost always operate under non-steady-state conditions. Start-up is of particular interest because it defines an upper bound of time to steady state for the system. Normal operation involves feed and product flow adjustments, which are much shorter term perturbations to the system. The simulated control scheme for ITER is similar to Princeton University's TFTR Tritium Purification System (TPS), which has recently been successfully commissioned. For the ITER ISS, dynamic simulation is important because it allows study of product quality control schemes and control system design. It also allows accurate assessment of tritium inventory variation in different operating modes. The cryogenic distillation model in the new DYNSIM code is described here in detail, including the underlying theory and numerical simulation approach. The discussion also addresses the suitability of different ISS design tools in terms of the design process, as well as HETP versus mass transfer modelling approaches.