Filtration apparatus for the assay of biological and biochemical reactants, for example, is provided and includes a substrate such as a plate having one or more wells open at each end, and a porous membrane positioned in each well forming a discrete filtering area. The filtration apparatus includes a seal that is in a compressible relationship with the face of the porous membrane, the surface of the compression element, and the well wall. Each well includes a compression element, such as an internal well insert or sleeve, which compresses the seal so that the seal contacts the membrane face, the surface of the compression element, and the well wall in a liquid-tight manner. The compression element may be configured so that it is fixed in the well such as by an interference fit with the well wall or by bonding to a surface of the substrate.