For drilling holes in soil or rock material and for fixing an anchor in a borehole, an expanding element fixed to a drill or anchor rod and a spreading element are introduced with the rod into the soil or rock material, the spreading element is expanded to butt against the wall of the borehole after completion thereof by the rod. The expanding element being retracted into the spreading element. The rod is secured by an anchor plate on an outer side of the borehole. After expansion of the spreading element, the rod is subjected to a rotary movement in the direction of the interior of the borehole until there is abutment with the interior of the borehole. The rod is fixed to the outside of the borehole by bracing the anchor plate by means of a nut.