The paper machine comprises a horizontal cylinder, a slurry feed box opening onto the top side of the cylinder and the upper rim of the feed slice of which has been continued in order to form a roof-like upper lip between the feed slice and a feed roll placed on the cylinder at an approximate distance from the feed box in the direction of slurry flow, an endless felt or wire running from the feed roll along the cylinder towards the lower part of the same, an appropriate number of guiding and tension rolls for conducting said felt or wire back to the feed roll, a suction box or suction roll placed on the side of the feed roll opposite to that facing the cylinder and at the point where the slurry web and felt or wire depart from the cylinder surface, and possibly a compressed air box or equivalent placed above the felt or wire and after the feed roll, as seen in the direction of travel of the wire, approximately coincident with the gap remaining between the roof-like upper lip of the feed box and the wire. The horizontal cylinder is a suction cylinder which has therein a suction zone extending substantially from and including the upper roof-like lip continuously to the suction box or suction roll. The upper roof-like lip and suction cylinder form a first drying area for the slurry to form a partially dewatered web while the belt thereafter contacts the web against the surface of the suction cylinder over a major portion of the descending surface of the suction cylinder to form a second drying area in which suction and centrifugal force act upon the web to remove additional water.