A tube extending along a tube axis is straightened by radially outwardly plastically deforming and expanding the tube by means of an expander mandrel and simultaneously bending the tube by applying radially inwardly directed forces to the tube at three points lying on a triangle. One of the points is level with the mandrel on one side of the tube and the other two points axially flank it in axially opposite directions and bear on the other side of the tube.