In a wet press for dewatering a web of material, for instance a web of paper, a contact pressure device presses against a rotating roll and exerts a pressure which increases in the travel direction of the web of paper. For this purpose, several rows of contact pressure elements are arranged sequentially in the travel direction of the web of paper. In each row the contact pressure elements are arranged side by side transversely to the travel direction of the web of paper. In order to circumvent a differential dewatering at the location of the contact pressure elements and at the gaps between the contact pressure elements of a row, the contact pressure elements of successive rows are shifted or staggered in relation to one another transversely to the web of material such that they mutually overlap. This prevents the arisal of strips in the paper being processed.