A pulp drying machine comprises a press (P1) and a circulation of a continuous supporting wire (2) that is permeable to water and that is introduced together with a pulp web (W) between press surfaces limiting a press nip, for removing water from the web towards the supporting wire (2). Dewatering means are provided on the opposite side of the pulp web (W), seen from the supporting web, for dewatering the web in the opposite direction. A circulation of a dewatering felt (1a) is placed within the circulation of the supporting wire (2) and introduced between the supporting wire (2) and the press surface that limits the press nip. The press surfaces of the press (P1) constitute a long nip.