The paper investigates the problem of constructing a system of models for an object with many input and output variables for the case of modeling the dependence of mechanical properties of a metal casting on the chemical composition of the raw materials. A technique for constructing system models for multidimensional objects from given experimental data is described The initial data set contains numerical values of five input variables (carbon, silicon, manganese, chromium, and phosphorus) and four output variables (tensile strength, relative elongation, impact strength, and hardness) characterizing the iron casting. Based on these data, the system of models is obtained describing the dependence of the output vector of casting properties on the input vector of its chemical composition and allowing to model these properties instead of conducting expensive experiments. To construct the system model, a technology of building models of multidimensional objects is applied based on the combinatorial GMDH algorithm allowing automatically derive linear or nonlinear models from a set of experimental data. As a result of modeling, a nonlinear system model of optimal complexity is obtained that allows explaining the dependence of the casting properties on chemical composition and the interdependence of these properties between them. This system model can be used for choosing the relevant chemical composition of raw materials for the specified physical and mechanical properties of the iron casting.