The invention concerns an apparatus allowing the bending of a glass pane, in such a way to have a even locally uniform bending radius. The apparatus comprises upper links (210) and lower links (310) between which a glass pane to be bend is positioned, at a suitable temperature as in the prior art. Below the lower links (310) a common axle (420) is placed, which put into rotation pinions (340) provided to each link (310). The pinion (340) makes a screw rotating and therefore vary the distance of contrast means (370,380) which abut on suitable stops (291) of the subsequent inner link, so as to adjust the maximum distance of the links (310) during the bending. The adjustment is obtained before the bending and is uniform because it is made concurrently and to the same extent on all the contrast elements of all the links. The invention further concerns an apparatus for bending a glass pane, with dynamical adjustment of the glass pane thickness.