Provided is an arrangement for cooling channels in an electrode column assembly of an electric arc furnace, wherein the lower part of the electrode column assembly is provided with a contact shoe ring formed of a plurality of contact shoe elements, a pressure ring formed of a plurality of pressure blocks, and a heat shield located above the pressure ring and formed of a plurality of heat shield segments. The contact shoe elements and/or the pressure blocks are provided with channels for a cooling liquid to flow therein. The channels made in the material of the contact shoe elements and/or the pressure blocks extend obliquely downwards from the upper ends of said contact shoe elements and/or the pressure blocks near to the lower ends of the same. At least two of said oblique channels join together at their lower ends to form a continuous channel.