Abstract: In combination with a lathe holding and slowly revolving, about its longitudinal axis, a work-piece to be screw-threaded with a tapering portion and a cylindrical portion, a tool holder ring is eccentrically mounted about the work-piece and is rapidly rotated about the work-piece in the same direction as the work-piece but at a relatively higher speed; while rotating, the tool holder ring is caused to advance longitudinally along the revolving work-piece; a plurality of cutting elements, radially secured in the holder, have cutting edges that intermittently and successively contact tangentially the work-piece during each revolution so as to move from the work-piece a chip with each revolution; the cutting elements are disposed in a series of planes and the number of planes is equal to the length of the tapering section divided by a pitch of the thread plus one, the depth of the thread being accomplished by the continuous chipping of subsequent cutting elements set on adjacent planes of the tool holder ring.