This paper presents a two-dimensional model for identification of the phase change front in a continuous casting process. The transport phenomena encountered in the considered process are solved by Boundary Element Method (BEM). For the known set of external boundary conditions, the whole problem is solved in two subdomains separated by a phase change front whose position is updated during the iteration process. The solution scheme involves the application of a front tracking procedure based on using sensitivity coefficients to find the correct position of the phase change front modelled by Bezier splines. The main features of the developed algorithms were investigated by several numerical tests, the most important results of which are presented in this article.