Flexible-membrane plate-and-frame filter presses are used by many industries to dewater compressible slurries. The dewaterability of such materials is described well by compressional rheology theory. The one-dimensional numerical model of fixed-cavity plate-and-frame filtration described recently (Stickland et al. Chem Eng Sci. 2006;61:3818-3829) is extended here to include the squeeze phase employed by flexible-membrane filter presses. The model is validated by comparing full-scale plant data from an industrial waste slurry with model predictions based on the fundamental material properties of the feed slurries (measured using laboratory-based filtration tests), the operating conditions and the press dimensions. The model is then used to investigate the optimization of the throughput and final cake solids for flexible-membrane filter presses. By providing an accurate model based upon the material propel-ties under the filtration environment seen by the material, the need for pilot-scale tests is eliminated. (c) 2007 American Institute of Chemical Engineers.