This paper concerns the mathematical and numerical modeling of solidification process of pure metals. Such process takes place without development of "mushy zone", which very often occurs during solidification of alloys. The model is based on the finite element method (FEM) and takes into account the existence of a sharp solidification front which moves according to time. The paper discusses how to include the conditions of continuity on the moving interface as well as the technique of front tracking based on the level set method (LSM). The paper also presents the results of computer simulations of the solidification process of pure copper. Two in-home solvers for one- and two-dimensional problems were built. Both of them are based on FEM. The correctness of the front tracking technique was checked by comparing the results obtained from 20 simulation to 1D simulation. Furthermore, the final calculation process was done for the two-dimensional area at different temperatures on the boundaries to demonstrate the effectiveness of the solver for a complex shape of the solidification front. (C) 2012 Elsevier Ltd. All rights reserved.