Abstract: An apparatus for dewatering aqueous materials such as a suspension, e.g. a slurry, by continuous pressing of the materials under high pressure. The dewatering is carried out in transport of the suspension between two driven webs which exert a pressure against the suspension, the latter by enclosing the webs at least partly about at least one press roll being subjected to an increased pressure by the enclosure to increase the dewatering effect, and at least the outer web relative to the press roll being pervious to the pressed out water content.