Abstract: When drying a paper web (4) in a dryer section (1) of a paper machine provided with drying cylinders (2, 3) and drying wires (5, 6), shrinkage of the paper web in cross direction is counteracted by applying forces at its edge portions (11). According to the invention partial vacuum is maintained along the edge portions of the web within substantially the entire free draw (10) and is applied from the side of the drying wire (5, 6) facing away from the web (4) so that the web is sucked firmly against the drying wire by forces greater than the contracting forces acting in cross direction, thereby counteracting shrinking, said partial vacuum being set within the interval 0.1-0.8 bar, preferably 0.2-0.5 bar.