Metallic pieces of predetermined shape, e.g., anodes, are continuously manufactured from molten metal, e.g., impure molten copper, by continuously casting the molten metal in an inclined mold cavity (13) formed by two endless moving belts (14( and (15) and by two moving side dams (20) and (21) so as to produce a hot metallic strip (4), and by cutting the hot strip, when it has left the mold cavity, with at least one plasma torch (10) along a profile (27) such that anodes (11) with a low waste coefficient are obtained. In this way, flat copper anodes with a thickness of between 40 and 50 mm can be produced.