This paper essentially deals with modeling of the concentration polarization effects on solute separation in ultra-filtration. Laminar tangential flow in a rectangular section channel is considered. The concentration polarization phenomenon in ultrafiltration has been studied by different authors who used different approaches for the finite-difference discretization of the mass transport differential equation. Two of those approaches are examined in detail. It is shown how numerical convergence can be reached, with a small number of increments, when an appropriate choice of the discretized mass transport equation is done. It is also shown why erroneous results have been obtained even with a large number of increments. Parametric studies show a strong influence of the true separation and of the permeation velocity on the separation profile along the tangential flow channel. A comparison between a finite-difference solution and an analytical solution for the mass transport differential equation is presented. Good agreement between the two methods is shown for the limiting case of high separation.