Current mammalian embryo cryopreservation protocols typically employ an interrupted slow freezing (ISF) procedure. In general, ISF consists of initial slow cooling, which raises the extracellular solute concentration, and results in cell dehydration. Permeating cryoprotective agents (CPAs), such as dimethyl sulfoxide (DMSO), are typically included in the medium to protect the cells against high solute concentrations. As this ISF procedure continues, slow cooling is terminated at an intermediate temperature (T_p), followed by plunging into liquid nitrogen (LN₂). If the slow cooling step allowed a critical concentration ([CPA]_c) of CPA to be reached within the cell, the CPA will interact with the remaining intracellular water during rapid cooling, resulting in the majority of the intracellular solution becoming vitrified and preventing damaging intracellular ice formation (IIF). This study presents a theoretical model to develop efficient ISF procedures, on the basis of previously developed data for the rat zygote. The model was used to select values of initial CPA concentrations and slow cooling rates (from initial estimated ranges of 0 to 4 molal DMSO and 0 to 2.5°C/min cooling rates) that would allow the intracellular solute concentration to exceed the critical concentration. The optimal combination was then determined from this range based on minimizing the duration of slow cooling.