Abstract: Arrangement for the electrospark working of internal conical surfaces of metal parts having a hollow space with a high slenderness ratio, terminating in a conical surface. The working electrode is guided in the hollow space of the workpiece and is provided with a simple and effective system of advance of the electrode, with the possibility of stoppage of the operation of the apparatus if due to some non-conductive dirt between the electrode and the worked surface correct operation is impossible, and with the provision of effective rinsing of the burning products.