A mathematical model of a mineral melting cupola furnace is used to illustrate the effects of different process parameters on furnace operation. The parameters studied include oxygen enrichment in the blast air, coke reactivity and coke size, and melting point temperature and heat capacity of the raw materials. The model is further compared to experimental data and general guidelines for cupola operation at stone wool factories. The comparison with the general guidelines indicates that the model captures the essential phenomena in the process and describes gas concentrations, temperatures, and flow rates inside the cupola well.