Controlling and optimizing smelting processes in submerged-arc furnaces are complicated by the limited amount of information available regarding the internal conditions. Computer models can help to bridge this knowledge gap. Due to the process complexity, computer models are commonly restricted to electrical conditions, thermal conditions, or chemical reactions, for instance. We have developed an overall model for a pilot-scale silicomanganese furnace that simultaneously considers electrical and thermal conditions, process chemistry, and flow of solid and liquid substances. To the best of our knowledge, this is the first comprehensive silicomanganese furnace model. The model has been compared to experimental data. Using information about the inner state of the furnace provided by the model, we are able to predict and explain an increase in temperature during over-coking as well as changes in the product compositions.