Abstract: Machine for cutting by electrical discharge machining includes an electrode wire tensioned between and running betwee two guide heads each of which is mounted on an arm, one at least of the arms passing through a hole in one of the walls of a tank. The tank can move with respect to the arm and contains a machining liquid. A sealing plate 1 masks the hole in the tank and is linked by at least one seal 4 to the arm 5 through the wall. The wall 2 of the tank through which the arm passes slides along this plate. To prevent the forces due to friction and pressure arising between the plate 1 and the wall 2 and between the seal 4 and the arm 5 and acting asymmetrically on the arm through the wall being transmitted to the arm 5 and causing its deflection, a sheath 6 is mounted between the seal 4 and the arm 5 and encloses this arm without coming into contact with it.