Drawn bores similar to a sleeve and provided with an inner thread are used as a substitute for nuts. The starting materials are flat sheet-metal blanks. In the course of step-by-step deformation with shaping tools, the wall thickness of the drawn bores decreases, compared to the starting material. This is true in particular with increased height of the drawn bores and sheet-metal blanks with larger surfaces. Accordingly, the invention is intended to recite a method according to which it becomes possible to produce high drawn bores, having a wall thickness comparable to the thickness of the original material, from sheet-metal blanks with large surfaces for highly stressed screw connections. This object is attained by means of a changed sequence of the step-by-step operation. Flat pressing of the sheet-metal piece is only performed after partial inward crimping has been started. This means that, unlike previously, the border area no longer is first fixed and maintained in a dressed condition during deformation, but is included in the deformation process and then is subsequently dressed again. The invention is of particular importance for metal construction work, namely for the manufacture of vehicles and apparatus.