A molded tool structure has a non-metallic body and a continuous band of flexible and resilient non-metallic material encompassing the body and bonded to its exterior surface. The body may be a tool or a tool part. Also, the body may have one or more metal inserts insert molded therein, in which case there is a band encompassing each such insert. In one embodiment the body is a socket with inserts at both ends and in another embodiment the body is a driver shank with a double-ended screwdriver bit having a Phillips tip insert molded in the body and a flat-blade tip projecting from the body. The tool structure is molded by placing the flexible and resilient band or bands in a mold cavity, the body material being injected into the cavity so that it flows inside the band or bands and forces each band against the mold at the peripheral of the cavity. Any inserts are positioned in the cavity on suitable fixtures inside the bands so that the material flows between the bands and the inserts.