A pressure filter includes two continuous mating surfaces movable relative each other and a filter medium capable of being disposed therebetween. A surface, provided for supporting the filter medium, is bounded by and is substantially coplanar with one of the continuous mating surfaces. The filter further includes a shallow inlet cavity, bounded by the other of the continuous mating surfaces, and an inlet distributor in communication with the inlet cavity. The inlet distributor includes at least one opening and may be of internal or external type. When the mating surfaces are pressed together, a shallow filtration chamber is defined by the inlet cavity and the filter medium. The filter apparatus may include a plurality of shallow filtration chambers, stacked one above the other, and constructed as described above.