The aim of this study is to predict the cryoinjury that is caused by thermal stresses during cryopreservation of living cells, tissues and organs. A thermal stress analysis model is developed for water freezing process taking place inside acolumn. The model allows us to predict the temperature field and the thermal stress distributions in the ice. The maximum tensile stress occurs during phase change. The radial stresses are less than the circumferential stresses and axial stresses. A quick freeing process results in larger thermal stresses in the ice than a slow freeing process does. When the cooling rate is IK/min the maximal stress is 0.12Mpa; when the cooling rate is 12K/min the maximal stress is 0.6Mpa. If the maximum tensile stress exceeds the failure strength, the crack will initiate on the wall of blood vessel.