The invention relates to a membrane filter press. On operation of such a press a secure generation of the necessary pressing pressure can be guaranteed with a membrane filter press comprising at least one membrane filter plate (1), a baseplate (3) with thickened edge region (4), a membrane (6) made from an elastically-deformable material and a filter cloth (7), whereby the membrane (6) comprises an annular edge beading (9) which lies in a complementary groove (8) on the baseplate. A sealing groove (29) is also let into the baseplate which opens out into the groove (8) at both ends in the manner of a bypass. A complementary sealing projection (30), moulded on the annular beading, engages in the sealing groove with formation of a seal. The cavity enclosed between the groove and the sealing groove is preferably provided with at least one filtrate drain drilling (23).