A direct current arc or resistance melting furnace includes a contact electrode produced as an exchangeable assembly outside the furnace and introduced into an opening provided in the bottom of the furnace tank. An annular gap between a refractory lining of the furnace tank and the contact electrode assembly is tamped.For exchanging the contact electrode assembly, it is detached from the lining with the aid of pressure elements (telescoping cylinders) arranged below the furnace tank and lifted upward far enough for the contact electrode to be pulled out of the furnace tank by the grip of a pulling device. Then a new contact electrode assembly is inserted.