A model of fixed-cavity plate-and-frame filter presses is developed based on the theoretical framework developed by Buscall and White (1987. The consolidation of concentrated suspensions. Part 1. The theory of sedimentation. Journal of the Chemical Society. Faraday Transactions. I, Physical Chemistry in Condensed Phases 83, 873–891) and the piston-driven filtration model of Landman et al. (1991. Dewatering of flocculated suspensions by pressure filtration. Physics of Fluids. A, Fluid Dynamics 3(6), 1495–1509). The model properly accounts for compression of the suspension network structure within a filter cake in one dimension over a fixed cavity and allows for the effect of membrane resistance and ramping pressures. The model is validated by comparing on-site measurements of actual process performance at two water treatment plants with model predictions based on fundamental material properties of the feed slurries, the operating conditions and the press dimensions. The material properties are measured using laboratory based filtration tests. The model is then used to investigate the optimisation of press throughput and cake solids for a ferric water treatment slurry.