A filter press comprises a plurality of membrane filter plates each comprising a base plate and an elastic membrane on at least one side of the base plate. The base plate has a circumferential raised plane edge portion surrounding a recess with a step-form recessed circumferential surface between the raised edge portion and the recess and a groove in the recessed circumferential surface and the raised edge portion. The membrane has a reinforced edge poriton of angular cross section with a first web lying on said recessed circumferential surface of the base plate and having a bevelled edge engaging the shoulder between the recessed circumferential surface and the raised edge portion and a second web received in the groove to provide a seal between the membrane and the base plate. The outer surface of the first web is recessed below the plane of the raised edge portion of the base plate. The base plate may have a flat-top support projection in the recess, in which case the membrane has an opening with a reinforced edge to accomodate the support projection. A seal is provided between the membrane and base plate around the support projection in the same manner as around the circumference of the base plate and membrane.