The invention relates to a method for producing a polymer motor vehicle component (2), in particular an outer add-on part in the form of a bumper, spoiler, sill, mud guard or the like. First of all, a polymer body shell part (6) is produced, preferably by means of an injection-moulding method, wherein, then, at least one aperture (3) is produced in the body shell part (6), optionally by means of a first automated method step, the aperture then defining an inner border (7) of the body shell part (6), and wherein, then, in a separate, second automated method step, a stamped formation (R) of a radius onto the peripheral edge (9) formed by the outer body shell-part surface (8) and inner border (7) and/or onto an outer edge formed by the outer border of the body shell part (6) takes place by a stamping tool (10) having a contour corresponding to the desired radius (r); of the stamped formation (R) being pressed along the inner border (7) against the peripheral edge (9) and/or along the outer border of the body shell part (6) against the outer edge.