Abstract: The method of making a round-rolled part for a heat exchanger comprises connecting the tubes and the irradiating elements to each other to form a rectilinear network, clamping both ends of the rectilinear network and stretching and bending the clamped network so that it assumes an arcuate shape. The premise adopted is that of a network of flat tubes consisting of rectangular tubes and irradiating elements between them, the tube network being bent round around a narrow side of the tubes. The network has one end rigidly gripped on the bending tool. The tubular network is wound onto it by rotating the latter. There is applied to the other end of the network a retaining force which counteracts the winding-on force and which maintains the tube network under tensile stress. The apparatus comprises a rotatable round bending tool and a clamping means which tangentially clamps the end of the network. Spaced from the round bending tool there is a mating holder for firmly gripping the other end of the network.