Accurate numerical prediction of freezing processes for meats is difficult. One of the reasons is the effect of heat transfer direction during freezing. When meat is being frozen, heat can transfer parallel to or perpendicular to muscle fibres of meats at various rates. In this study the influence of the heat transfer direction on the numerical simulation of the freezing processes was analysed. A computer simulation program using the modified Crank-Nicolson finite difference scheme was developed to predict the temperature profiles during freezing. Two thermal conductivity formulas, the Levy and the modified series equations, were incorporated into the program. Experiments were carried out on beef samples. The comparison between the numerical results and experimental data shows that the program can predict the freezing processes well.