Abstract: There is developed a burr processing apparatus in which a discharge electrode is moved along a peripheral edge of the processed material, the burr is processed in an entire uniform manner and concurrently the arc discharge is performed stably and a long life of the electrode is attained. The burr processing apparatus of the present invention is made such that the discharge electrode 20 is formed into a cylindrical shape having a sectional shape gradually narrowed toward the extremity end and having a specified width in a lateral direction, the discharge electrode 20 is kept at a height suitable for the arc discharge, the case 30 is arranged to cover the electrode, the handle 40 is connected to the case 30 to be moved manually and a power supply for the arc discharging is connected to the discharge electrode 20.