A flexible shaft coupling is comprised of a tubular hub made of a rigid material, wherein the hub is provided with a slit extending substantially circumferentially for providing flexibility to the hub, the hub having an axial bore so that a rotational force of a drive rotation shaft received in the axial bore at one end of the hub can be transmitted to a driven rotation shaft attached to the other end of the hub, wherein circumferential ends of a part of the hub adjoining the slit are each provided with a convex shape having an arcuately receding surface at least at an outer peripheral portion.