A mathematical model has been developed to study the process of freezing in biological organs. The model consists of a repetitive unit structure comprising a cylinder of tissue with an axial blood vessel (Krogh cylinder) and it is analysed by the methods of irreversible thermodynamics. The mathematical simulation of the freezing process in liver tissue compares remarkably well with experimental data on the structure of tissue frozen under controlled thermal conditions and the response of liver cells to changes in cooling rate. The study also supports the proposal that the damage mechanism responsible for the lack of success in attempts to preserve tissue in a frozen state, under conditions in which cells in suspension survive freezing, is direct mechanical damage caused by the formation of ice in the vascular system.