A method for manufacturing a tube made of a non-ferrous material, particularly a tube made of mainly copper, by rolling, in which method, in the first working step the tube billet is worked by rolling with conical rolls, so that mainly owing to the deformation resistance, the temperature of the billet under operation rises up to the recrystallization range, at least on the spot that is being worked. Essentially immediately after the first working step, the tube billet is subjected to at least one second working step with a second set of conical rolls, in which case the tube billet is maintained, at least during the first working step and at least a second working step in non-oxidizing conditions. The invention also relates to an apparatus.