Abstract: A process for forming a prestressed anchorage by drawing a steel sleeve over a metal core of elongate shape having a substantially round section, consisting in using a sleeve having an inner diameter substantially equal to the outer diameter of the metal core, in forming a grooved portion or indentations in the inner cylindrical surface of the sleeve, in subjecting the inner cylindrical surface of the sleeve and its grooving to surface heat treatment adapted to increase the hardness thereof and to give thereto a value greater than that of the metal core, by causing the tempering depth to increase from one end to the other of the sleeve and in anchoring the sleeve on the metal core, in a way known per se, by drawing the sleeve through a draw-plate.