The calculation of the flux/pressure drop relationship for polymeric membranes using the Hagen - Poiseuille relationship takes only the pore size and membrane depth into consideration, and fails to consider the internal cellular structure. The understanding of the structure of such membranes has been achieved by scanning electron microscopy (SEM) and image processing techniques, and with such a complex internal structure it is clear that further consideration of the cellular polymeric mesh must be included. A stochastic three-dimensional (3D) geometric model is used to simulate these structures. Predictions of the pore properties are in goad agreement with data obtained by image analysis of SEM photomicrographs. The clean membrane flux variation with pressure drop is predicted by considering creeping viscous flow past an array of oblique cylinders, where the pore edges are assumed to be cylindrical in shape. Excellent agreement between the theoretical predictions and experimental results has been achieved for the membranes studied. The stochastic model is used to predict the transport of latex slurries in dead-end pressure filtration. This has been developed to predict a surface cake and the penetration of particles into the membrane. It is possible to predict the importance of the particle diameter to the pore size rating and the position of fouling in the membrane. Graphical images are compared to photomicrographs, to obtain knowledge of the steric interactions between particle-particle and particle-pore collisions within and on the surface of the membranes studied. In addition, the model is capable of extension to other forms of cellular porous structures.