Abstract: A method of bending a long metal member of constant cross-section by locally heating a narrow zone on the periphery of said member by means of a heating collar (5) which surrounds said zone, by exerting thrust (2) on one end of the member and by supporting its other end by means of a pivoting arm (3). The temperature of the heated zone on the periphery of the member is kept substantially constant by detecting the temperature of this zone or the size of the gap which separates the heating collar from the periphery of said zone at at least two points around said periphery, one of these points being nearest the center of curvature and the other being on the opposite side to the first.