The development of a computational simulation system for modeling the solidification process in a continuous casting facility for steel slabs is discussed. The system couples a module for solving the direct problem (the calculation of temperatures in the steel strand) with an inverse analysis module that was developed for evaluating the steel/mold heat fluxes from the information provided by thermocouples installed in the continuous casting mold copper plates. In order to cope with the non-uniqueness of the inverse analysis, a priori information on the solution, based on the consideration of the problem physics, is incorporated. The stability of the system predictions are analyzed and the influence of the first trial used to start the evaluation procedure is discussed. An industrial case is analyzed.