Abstract: A method and apparatus for polishing a workpiece by electrical discharges by way of an electrode tool, machining pulses of relatively low power being obtained from a machining pulse generator. A cross-slide table provides the workpiece with a translation cyclical motion during polishing. Input control circuits enable the machine operator to program a chosen speed of translation for the cyclical motion, the radius of circular translation and the time of duration of machining. A counter counts the number of cycles being effected and a discriminator stops the pulse generator as soon as the chosen number of desirable cycles is obtained, such number being inversely proportional to the amplitude chosen for the translation motion.