To provide a burner for combusting plastics for use in an arc furnace which is able to effectively utilize the heat obtained by the combustion of the plastics in the furnace.

The arc furnace for melting and refining metallic materials in the arc furnace comprises a channel for pneumatically conveying the plastics by air or the like and blowing the same into the arc furnace and the combustion burner comprising a fuel channel for oil, gas or the like, and an oxygen channel on a water-cooled wall of the arc furnace main body having the circumference thereof constituted of the watercooled wall. In the method of melting and refining the metallic materials in the furnace, cooling water is circulated in the water wall and then the temperatures at the exit and entrance for the circulating water are measured. When the temperature difference between the entrance side cooling water and the exit side cooling water begins to become smaller, plastics are blown from the combustion burner.