Abstract: A socket tool for alternative use in combination with a screw driver or a conventional wrench. A socket body is formed so as to fit externally over a driver bit and is movable axially therealong and is detachable therefrom but is non-rotatable relative to the driver bit over its length. Socket portions are provided on opposite end portions of the socket body, with internal dimensions different from one another. Outer peripheries of the socket portions at both ends of the socket body are formed into regular polygonal shapes in cross section and serve as external drive engaging faces, to be engaged externally by the wrench. The outer peripheries of both the socket portions have external diameters different from one another. The socket tool is held alternatively on either the driver bit or the wrench, with one of the socket portions engaging the driver bit or wrench and the other socket portion projecting longitudinally away therefrom.