Abstarct: In this study, the phase change and heat transfer process in continuous casting machines analyzed. The mold, which use in this problem is column and the cross section is square. In the current work, by choosing a suitable cylindrical coordinates we are able to simplify the problem and transform the equation into an unsteady one-dimensional energy equation. In the case of solidification in continuous casting process, the boundary of the domain is not known in advance. This means that the solution of such problems requires solving the diffusion or heat conduction equation in an unknown region which has to be determined as part of the solution. Solution reported in the literature using the control-volume finite difference approach together with the boundary immobilization method is selected to predict the position of moving interface and the temperature distribution. Also an analytical solution for this problem is reported that using by variational iteration method. The approach is validated by some available models and the agreement is found to be satisfactory. Effects of the governing parameters such as Stefan number and casting speed on the evolution of the freezing front and temperature distributions are investigated. It is found that the variation of Stefan number has a strong influence on the growth of the shell thickness and the temperature distributions. For the same values of heat transferred from the mold, increasing Stefan number has significant results such as: accelerating the solidification process and increasing the solid thickness, enhancing the local heat flux in the liquid, and broadening the liquid zone affected by the cooling jacket. As the casting speed becomes higher, the molten flow leaves the mold faster and the solid thickness entering the secondary cooling stage will be decreased. Decreasing of casting speed results in decreasing the solid temperature; in other words, the solid laxyer becomes cooler. Increasing the casting speed causes the central region has less time to be affected by the cooling water.