Pleated membrane filters are ubiquitous in many industrial filtration systems, since they offer more surface area to volume ratio. However, it is known that the performance of a pleated membrane filter is usually inferior compared to flat non-pleated membrane filters with the same membrane surface area. Therefore, a question of interest to manufacturers is: What is the optimum initial permeability profile as a function of depth through the membrane in order to achieve the maximum filtered fluid while removing certain amount of contaminants from the solvent? In the first part of this talk, we present a mathematical model to describe the flow and transport in the complex geometry of a pleated filter. In the second part, we use the computationally efficient model to investigate how the filtration performance depend on the initial permeability of the membrane.