A method for manufacturing includes a polygonal shape closed structure part with a bent shape in the longitudinal direction only by press forming. The method uses two metal plates for manufacturing a curvilineal closed structure part and includes a press forming process of forming straight or bent folding lines in the longitudinal direction of the two metal plates at positions corresponding to a polygonal bent shape with a flange formed at least at one of the ends of the width direction of each plate, a process of forming a closed structure by laying the two metal plates to overlap each other flange to flange and end to end for ends without flanges and by welding the portions laid to overlap each other in the longitudinal direction of the metal plates, and a process of forming a polygonal shape closed structure having a bent shape in the longitudinal direction by holding both ends of the closed structure and by compressing it toward its central axis.