A non-linear cooling cryopreservation method for improving cryopreservation protocols for cells that involves producing a simulation of cellular responses to a range of cooling parameters; determining optimal cooling parameters required to minimize cryoinjury to the cells using simulation of cellular responses and experimental results; and incorporating optimal parameters into the protocol. The simulation is based on mathematical models of cellular parameters. A non-linear cooling cryopreservation protocol for cryopreserving stem cells is also disclosed that does not require cryoprotectants.