Abstract: As a new technique for manufacture of high-precision shaped seamless steel tubes, the non-mandrel/ rollextrusion forming process features low energy consumption, fine surface quality and pushing force in terms of force-applying way. Witht this process, tube formation is completed under a condition of three-directional pressure-stress, resulting in longitudinally restriction of elongation of the tube, good corner filling and minimum outer radius value R at the joint points between the sides as well as mush higher processing accuracy, and being. particularly applicable for manufacture of large-sized, heavy-wall or small-sized thin-wall precision shaped seamless steel tubes. Also described in the article is how to use the main stress method to establish the calculation formula for extrusion force applied to during non-mandrel/ roll-extrusion process of shaped seamless steel tubes