The goal of this study is to introduce the fundamental thermodynamic principles of isochoric (constant volume) cryopreservation for low temperature preservation of biological materials. Traditionally, cryopreservation is performed in an isobaric process (constant pressure) at 1 atm, because this is our natural environment and it is most convenient experimentally. More than half a century of studies on cryopreservation shows that the major mechanism of damage during isobaric cryopreservation is the increase in intracellular ionic concentration during freezing, which presumably causes chemical damage to the components of cells. Cryoprotectants as well as hyperbaric pressures have been developed as methods to reduce the extent of chemical damage during freezing. The theoretical studies in this paper show that in isochoric cryopreservation, the increase in solution concentration during freezing is lower at each temperature by almost an order of magnitude from that in isobaric cryopreservation. This suggests that isochoric cryopreservation could be a preferential alternative to isobaric cryopreservation. The technology for isochoric cryopreservation is very simple; freezing in a constant volume chamber. Using a simple isochoric cryopreservation device, we confirm the theoretical thermodynamic predictions.