The furnace of the present invention includes a body of a furnace having a cylindrical shape; a steel shell which is arranged at an inside surface of the furnace; and a lining refractory which is arranged at an inside of the steel shell and includes a plurality of refractory blocks, wherein: each of the refractory blocks includes a hot-face end surface which has a hexagonal shape exposed to a middle of the furnace, and a cold-face end surface which has a hexagonal shape larger than the hot-face end surface, the cold-face end surface being arranged at an outer periphery side of the furnace; the refractory blocks are arranged such that each position of the hot-face end surface is positioned along the radial direction of the furnace at a predetermined reference position; and the refractory blocks are arrayed along the circumferential direction of an inside surface of the steel shell, thereby being stacked in a honeycomb manner.