A mathematical model of a mineral melting cupola furnace for stone wool production has been developed for improving cupola operation. The 1-D, first-engineering-principles model includes mass and heat balances for the gas phase, five solid phases, and four liquid phases. The gas and solid/liquid phases flow countercurrently. Seven chemical reactions account for the conversions of coke, iron oxide, limestone, and gaseous species. The heterogeneous reactions of coke conversion are limited by both kinetics and mass transport. Heat transfer between phases is modeled including both convection and radiation. The model predicts gas concentrations; mass flow rates; and temperature profiles of the solid, melt, and gas in the cupola, as well as heat loss to the water-cooled walls. Inputs to the model include the coke, rock, and blast air properties, the blast air amount, and the coke percentage in the charge. The unknown model parameters are estimated on the basis of input/output measurements. A comparison of the predicted and measured concentration and temperature profiles inside the cupola shows good agreement.