As for the mathematics model of a blast furnace of Nippon Steel Corp., development has been mainly done centering on the model that estimated material transfer, reaction and heat transfer of lumpy zone or cohesive zone. In parallel with this, a burden distribution model, a reaction model of tuyre and raceway, a model concerning of deadman and of a furnace hearth are developed and approximately cover the whole blast furnace. These models have been used for the analysis and the operation design of actual operation. In addition, we are developing a model with a disintegration element method and a non-steady model recently.