Cryopreservation by vitrification is a promising technique for preservation of biomaterials such as organs for long term storage. Crystallization while cooling and warming is an important hurdle for a successful cryopreservation. This problem can be addressed by the use of cryoprotectant solutions (CPAs) which help in inhibiting crystallization. The cooling and warming rates needed to prevent crystallization in these CPAs are called Critical Cooling Rate (CCR) and Critical Warming Rate (CWR) respectively. Thermal modeling is an important tool which can help to study this process and predict subsequent cooling and warming rates needed to avoid crystallization. Temperature dependent thermal properties such as thermal conductivity, specific heat capacity and density are needed in order to develop an accurate model. This work involved the measurement of specific heat capacity (Cp) of high concentration CPAs (> 6M) that are used to study vitrification. The thermal properties were then used in a numerical model to predict cooling and warming rates encountered in a cylindrical geometry of CPAs. Chapter 1 provides a review of the thermal properties (thermal conductivity and specific heat capacity) of various biomaterials available in the literature in the sub-zero and supra-zero temperature ranges. Thermal properties of biomaterials are highly temperature dependent. In addition to dependence on temperature, these properties are affected by crystallization and vitrification at sub-zero temperatures (<0°C) and protein denaturation and water loss at supra-zero temperatures (>0°C). Finally, a modeling case study (Bischof and Han 2002) has been provided to highlight the significance of using temperature dependent thermal properties for accurately predicting thermal history. Chapter 2 focusses on experimental measurements of specific heat capacity (cp) of five high concentration CPAs (> 6M) — VS55 (with and without sucrose), DP6 (with and without sucrose) and M22. Further, the effect of cooling / warming rate (1, 5 and 10 °C/min) on crystallization and vitrification has been studied. It was observed that the addition of 0.6 M sucrose to two CPAs viz., VS55 and DP6 suppressed their crystallization for all the three cooling and warming rates. Chapter 3 involves thermal modeling of cooling and warming in a COMSOL Multiphysics package. Thermal properties from Chapters 1 & 2 were used in order to predict the cooling and warming rates for three conditions, viz. convective cooling, convective warming and nano warming. These simulations were carried out in a cylindrical geometry for an increasing size, i.e. the radius of the cylinder. The objective was to find the size limit beyond which cooling and warming rates would not exceed the CCR and CWR respectively.