The paper evaluates two approaches of numerical modelling of solidification of continuously cast steel billets by finite element method, namely by the numerical modelling under the Steady-State Thermal Conditions, and by the numerical modelling with the Traveling Boundary Conditions. In the paper, the 3D drawing of the geometry, the preparation of computational mesh, the definition of boundary conditions and also the definition of thermo-physical properties of materials in relation to the expected results are discussed. The effect of thermo-physical properties on the computation of central porosity in billet is also mentioned. In conclusion, the advantages and disadvantages of two described approaches are listed and the direction of the next research in the prediction of temperature field in continuously cast billets is also outlined.