The present invention relates to the thickening of pulp suspensions. A low consistency pulp suspension is fed to a pre-thickener (10) through an inlet conduit (18). A layer of thickened pulp, formed on a filter surface (22), is pushed along the filter surface by a cleaning member to the discharge end of the pre-thickener and is discharged through the outlet (20). The cleaning member comprises a rotating shaft (30), on which shaft at least one screw thread (32) is fixed so as to leave a free space between the shaft and the screw thread. Essentially non-thickened pulp is allowed to flow through the apparatus via this space.