A hypothesis of the nature of intracellular ice formation is proposed in which the osmotically driven water efflux that occurs in cells during freezing (caused by the increased osmotic pressure of the extracellular solution in the presence of ice) is viewed as the agent responsible for producing a rupture of the plasma membrane, thus allowing extracellular ice to propagate into the cytoplasm. This hypothesis is developed into a mathematical framework and the forces that are present during freezing are compared to the forces which are required to rupture membranes in circumstances unrelated to low temperatures. The theory is then applied to systems which have been previously studied to test implications of the theory on the nature of intracellular ice formation. The pressure that develops during freezing due to water flux is found to be sufficient to cause a rupture of the plasma membrane and the theory gives an accurate description of the phenomenology of intracellular ice formation.