The invention relates to a mould for the manufacturing of mould steels in an inert gas or a pressurized electro slag re-melting apparatus. The mould comprises a non-rectangular and non-circular inner copper sleeve having a width, w, of 1000-2500 mm and a thickness, t, of 700-1250 mm, wherein the short sides in the thickness direction of the copper sleeve at least partly have sections with curved surfaces and wherein the long sides in the width direction at least partly have sections with curved surfaces.