Using a continuum model for multi-component phase change system, the freezing of cell suspension in a ternary solution, H2O-NaCl-CPA (cryoprotective agent) inside a flat bag is investigated numerically in this study. The temperature and phase change history, intracellular water loss, and the volume change of the cells at different locations inside cell suspension are calculated. Numerical results reveal that although the sample boundary is cooled at a constant rate, different locations inside the sample experienced different temperature changes and cooling rates. The highest cooling rates occur at internal locations. The cell volume change is location-dependent.