Mathematical modeling of an ultrafiltration membrane separation process, based mainly on the transmembrane pressure (TMP), is undertaken in the present work. The main objective is the prediction of the permeate flux of a solution containing Dextran T500 through a cylindrical module. The proposed model incorporates the resistance-in-series model coupled with the equation describing the solute (Dextran T500) transport, as well as the continuity and Navier-Stokes equations for solution flow modeling. The model equations are solved using finite-volume numerical methods, with appropriate initial and boundary conditions. The effects of the TMP and the length of the membrane on the mean permeate flux were also investigated. The influence of the membrane dimensions (aspect ratio) on the relative dimensionless mean permeate flux, at different inlet TMPs and different solution concentrations, respectively, have also been considered. The variations of the TMP with the membrane length as well as the influence of the Peclet number on the solute surface concentration were also examined. The numerical results obtained are compared with experimental values reported in the literature, and in general, the agreement is satisfactory enough to encourage further refinement of the model.