In a filter press sediment is dewatered in filter chambers. The watery sludge is placed under pressure in chambers. The water from the sludge can flow away through a filter cloth via filtrate discharge channels. The solid is retained by the filter cloth. After a certain amount of sludge in the chambers has been accumulated, it can be removed by opening the chambers. This completes one processing cycle, and a fresh batch of material can be introduced into the press. In addition to the application of horizontal chambers, it is also possible to place dewatering units one above the other in order to save space (vertical filter press).