Abstract: For the working of walls which bound the cavity of a continuous casting mold, a machine is used which incorporates machining and/or polishing tools. The machine consists of a machine tool table with an arm introducible into the cavity for the supporting of the tools and a table for the clamping of the mold, as well as devices for generating a numerically controlled relative movement between the tools and the walls. In order to obtain a high accuracy in the working also in the case of a cavity with a conicity varying in longitudinal direction and/or along the peripheral line of a cross-section or in the case of a cavity with special corner configurations, it is proposed that a rotational movement of the tools about axes which are arranged substantially obliquely to the longitudinal axis of the arm be combined with a swivelling movement of the arm about its longitudinal axis.