A consumable electrode vacuum arc furnace and, more particularly, a direct current consumable electrode vacuum arc furnace is provided, wherein no water cooling is needed to cool down typically neither the electrodes, nor any other parts of the furnace, and this includes the shell, the flanges ports and the electrical connections of the furnace. The present furnace uses non-metallic electrodes, such as graphite electrode, which are suitable for melting metals, smelting of metal ores, and metal oxide to elemental metal where the use of graphite electrodes is a common practice. The present furnace and electrode assemblies render possible to perform a true continuous process of melting and smelting under controlled pressure.