A screwdriver for bone screws is provided, having a handle and rotationally fixedly held thereon a shaft, a free end of which has a non-circular cross section and is insertable in a positively locked manner in a non-circular receiving opening in a head of a bone screw. At least one expander element is mounted to be displaceable in a longitudinal direction in the shaft and to slide, when displaced, along a slide surface in an area of the free end of the shaft such that the at least one expander element projects laterally over a contour of the shaft. The non-circular cross sections of the receiving opening and the free end of the shaft are configured such that the shaft is pressed by the at least one expander element in two areas of the receiving opening that are separate from one another against an inside wall of the receiving opening.