Freezing is a very common method of food preservation around the world. Accurate simulation of the freezing process in food materials is very important for the design of superior freezing processes and more efficient refrigeration equipment. The accuracy of numerical methods is very significant for reliable prediction of temperature history in food materials during freezing. However, accurate simulation of the freezing process in foods is difficult due to its inherent nonlinearity. In this study, a technique was presented and used to assess the accuracy of the Crank-Nicolson and the Two-Step methods in solving this nonlinear problem. Overall, the accuracy of the Two-Step method was higher than that of the Crank-Nicolson method. These numerical methods were also implemented to simulate one-dimensional freezing experiments. Again, the results of the Two-Step method exhibited better agreement with the experimental data than the Crank-Nicolson results. The thermal properties of food materials change substantially with temperature during freezing. The estimation of these properties is very important in simulating freezing and determining the freezing time of foods. Mathematical modeling of the thermal properties of foods has been an appealing alternative to experimental methods. These models are generally based on the assumption that food materials are ideal binary solutions. One of the goals of this research study is to estimate thermal properties of aqueous solutions of basic food substances (sucrose, methyl-cellulose, and wheat gluten) during freezing. Temperature data from one-dimensional freezing experiments were used to estimate the temperature dependent thermal properties of these materials during freezing using the Modified Box-Kanemasu estimation method. The estimated thermal properties were then compared with models from the literature. Generally, the estimated thermal properties did not agree well with the predicted properties using the models from the literature, especially in the case of methyl-cellulose and wheat gluten. Hence, the models examined in this research study need to be modified to account for the chemical and the physical processes that occur during freezing. / Ph. D.