The steady laminar flow of a suspension of neutrally buoyant particles of non-colloidal dimensions, through a pressurized open-ended channel having microporous membrane walls, is studied in the context of crossflow microfiltration (Davis and Leighton, 1987, Chem. Engng Sci. 42, 275-281). Fully developed, Poiseuille flow is assumed in the bulk of the suspension whereas the filtrate crossflow velocity through the membrane walls, V-w, is taken to be much smaller than the average downchannel velocity, U-0, and is assumed to be constant for all practical purposes. It is shown that in the limit as a/L --> 0, where a is the characteristic particle radius and L is the characteristic length scale along the channel walls, the particle concentration remains uniform throughout the channel except for two O (a(2)L)(1/3) regions, near the two channel walls, where convection and shear induced particle diffusion balance each other. The system of equations within these two regions admits a treatment analogous to that presented by Pelekasis and Acrivos, 1995, (J. Fluid Mech. 293, 301-321) in their study of sedimentation and convection past a flat plate. In the present study particle filtration takes the place of sedimentation while the constant shear rate imposed by the poiseuille bulk flow replaces the Blasius velocity profile. The main goal of the study to be presented is to predict the critical length along the channel walls needed for the particle concentration at the wall to reach its maximum value phi(m) = 0.58, and consequently for the formation of a stagnant sediment layer. A similarity solution is obtained near the entrance of the channel which predicts an increase of the particle concentration by an amount proportional to X-1/3, with X measuring the distance from the entrance. For values of X beyond the entrance region a numerical solution is obtained which provides the prediction for the critical length over a wide range of bulk particle concentrations, phi(s). Asymptotic results are derived for the cases phi(s) --> 0, and phi(s) --> phi(m). It should be noted that, in the limit phi(s) --> 0, the model employed by Davis and Leighton (1987, Chem. Engng Sci 42, 275-281), in one of the first theoretical approaches that accounted for shear induced particle diffusion in crossflow microfiltration, is recovered. Finally, as a demonstration of the validity of our approach, the results of the present study are shown to compare favorably with the experimental findings by Davis and Birdsell.