Abstract: The aim of this study was to predict the cryoinjury that was caused by thermal stresses during cryopreservation of living cells, tissues and organs. A thermal stress analysis model is developed for water freezing processes taking place inside a ball. The model allows us to predict the temperature field, moving phase interface location and the thermal stress distributions in the ice. A quick freezing process results in larger thermal stresses in the ice than a slow freezing process does within a certain level. Above this level, the freezing rate has no effect on the thermal stresses.