The invention relates to a self-boring and thread-forming tapping screw having a screw shaft with a screw tip at one end and at the other end a force application member for the transmission of a turning moment. The screw shaft includes a threaded section with the screw tip and an adjacent thread-free section of the shaft including the force application member. The threaded section has a shaft core and a self-tapping thread. The threaded section includes a core section axially displaced from the tip and having a polygonal core cross section. Corners of the core cross section define an enveloping circle with an enveloping circle diameter larger than a shaft diameter of the thread-free section.