Pressure filtration is a common industrial process used for solid-liquid separation and laboratory technique used to measure the compressional theological properties of suspensions. Traditional approaches to the modeling of constant pressure filtration behavior of particulate systems stipulate quadratic behavior of time with filtrate volume. However, this is not necessarily a fundamental attribute of pressure filtration, but rather a result of the assumptions made of the compressibility and permeability of the material. This work solves diffusion-type constant pressure filtration governing equations using a finite-difference technique to demonstrate that filtration, under certain circumstances, is expected to show negligible quadratic behavior. Materials that exhibit such behavior have often been classified as nontraditional and methodologies have been developed to interpret such trends. This work illustrates that such behavior is in fact covered by extant filtration models and does not require any extra interpretation of the forces involved. Furthermore, it is shown that traditional or nontraditional behavior is dependent on the initial solids concentration and the applied pressure, such that the filtration of a suspension may show relatively long cake formation times at low initial concentrations or pressures, and relatively short times at high initial concentrations or pressures. (c) 2005 American Institute of Chemical Engineers.