A press forming method forming an extended part by extension in a later forming period after deep drawing, the deep drawing process carried out with working at 100-250° C., and the extension forming process carried out colder at less than 50° C., whereby the extended part is formed by extension in a cup shaped low parts formed by deep drawing. Thus, press forming products containing formed elements can be deep drawing formed and extension formed at a high forming rate of 10 mm/sec or greater, which can assure high productivity. By making a steel plate temperature 100-350° C. during press forming and by making the forming rate in the later forming period where extension forming is carried out slower than the forming rate in an earlier forming period where extension forming is not carried out, cracking of the extended part can be prevented and press forming limitations can be improved.