Abstract: A flexible coupling is provided for use between the shaft of a screw pump rotor and that of a driving motor where the shafts are required to transfer considerable axial forces and are subject to rotating out of axial alignment with each other. The respective shaft ends are formed either as cones or sections of spheres and are held together by a screwspring which envelopes both ends and transfers much of the torque from one shaft to the other while reducing the possibility for lateral displacement of the shafts. The shaft ends are positioned to roll against each other to reduce wear when the shafts rotate.