Abstract: Apparatus for tapping or threading holes in material reduces stresses and the danger of breakage of the tap by rotatably driving the tap at locations on the tap that change as the tap enters the workpiece. The driving element engages the tap at a point close to the surface of the workpiece. As the tap advances into the workpiece, the driving element remains close to the workpiece surface, engaging the tap at sites progressively advancing toward the end of the tap. Special taps are provided, one of which is double ended. This may be turned end for end to double the useful cutting life. This embodiment is driven by its flutes. Another tap is driven by a non-circular shaft extending from the threaded portion of the tap. The taps may be removed from the workpiece by passing through the threaded hole, thereby eliminating the need to unscrew the tap through the already tapped hole.