Abstract: A process for continuous casting of hollow ingots wherein the rate of heat removal from the surface of an ingot within a mold is changed gradually over the mold height from a given maximum value in the ingot skin formation zone to a given minimum value as the ingot emerges from the mold. The speed of the continuous ingot withdrawal from the mold is increased gradually during each withdrawing cycle from zero to the maximum value for apredetermined length of time. An apparatus in accordance which comprises a water-cooled mold which is made in the form of an inverted truncated cone with the diameter of any of its bases being substantially less than its height. A part of the upper portion of the mold being cylinder-shaped and formed with a plurality of slots. The diameter of projections formed by the slots is slightly less than that of the top base of the frustoconical section, with the walls of the slots passing smoothly into projections.