A method for fastening a component to a base element, in which method there is produced in the base element a blind bore which defines a depth direction and which has a force transmission surface which has a depth T in the depth direction, wherein the force transmission surface is of frustoconical form with a cone opening half-angle (β) and a mean diameter (d), wherein the blind bore has a conical blind bore base with a cone opening angle (α) and, at the edge thereof, a bevel which extends in the depth direction to a bevel depth L, wherein, in the method, a fastening element is anchored in the blind bore by way of the force transmission surface, and wherein the component is held by the fastening element.