An apparatus for washing and dewatering pulp comprising a first and a second rotatable press roll (102, 104) having a permeable outer surface (108, 108), and a casing provided with a vat (114, 116, 118) in which the press rolls (102, 104) are installed, the vat (114, 116, 118) partly enclosing the outer surface (108, 108) of each press mil (102, 104) and a gap (124) is formed between the vat (114, 116, 118) and the outer surface (108, 108) of the press rolls (102, 104), the press rolls (102, 104) defining a press nip (112) between them, in which press nip (112) the pulp is pressed, and the apparatus is arranged to feed the pulp in the gap (124) in the direction of rotation of the press rolls (102, 104) and through the press nip (112), and the vat (114, 118, 118) comprises at least one vat segment (114, 118, 118). At least one compartment (119) is provided between the at least one vat segment (114, 116, 118) and the casing, said compartment (119) extends along the longitudinal extension of at least one of the press rolls (102, 104), and the apparatus comprises means for attaining a pressure in the compartment (119) which corresponds to the pressure in the gap (124).