Apparatus for filtering liquids, comprising flat membrane pockets arranged parallel and means for pressure-tight connection of the membrane pockets to one another and for coupling an extraction means. The membrane pocket includes a drainage element, which is joined surface-to-surface to two membranes and is enclosed in a pressure-tight manner at the edge. Adjacent membrane pockets are connected to one another and to the extraction means via one or more outflow bores and associated lines. The outflow bores are arranged in such a way that the transmembrane differential pressure drops only slightly over the surface of the membrane pocket.