Abstract: A pressure roller in a winding machine is axially shifted in accordance with the progress of winding so that the winding turns are tightly engaged with each other. At the end of a winding layer, the pressure roller is positioned adjacent a flange of the winding drum at a spacing distance equal to 1.5 times the diameter of the round material, so that the next winding layer is wound in the channels between winding turns of the first layer. The pressure roller and the winding drum are axially shiftable independently of each other, thereby providing centering of the drum with respect to the in-feed material and orderly reversal of winding action after each winding layer has been completed. The method and the apparatus are particularly suitable for thick round material which is hard to flex, such as solid or stranded wire or cable.