This paper represents a numerical investigation of the hydrodynamics and mass transfer operative in antipolarization dialysis (“APD”), a novel concept for fractionation in which adjacent countercurrent flow streams are (i) separated by a longitudinal solute-selective membrane, and (ii) pass through upstream and downstream “barrier” membranes that reject all solutes. Selectivity of the process—embodied in the sensitivity of steady-state concentration profiles to Péclet number and membrane transport resistance—has previously been analyzed (Nitsche, L. C., 1994, Quart. Appl. Math., LII, 83–102) using the simplifying idealization of plug flow. Practical considerations of construction require the barrier membranes to be positioned longitudinally instead of transversely, so that the corresponding ultrafiltration flows occur perpendicular to the fully developed, parabolic velocity profiles in the channels. These hydrodynamic end effects are modeled numerically using a least-squares boundary singularity method that explicitly incorporates the analytical structure of discontinuities in the flow field arising at the junctions between porous and impermeable boundaries. Subsequently, the impact of flow nonidealities upon the transport of solute is addressed by applying finite differences to the relevant elliptic convection-diffusion equation for the concentration field. Calculations at large values of the aspect ratio take advantage of the singular asymptotic structure of the problem, whereby only the “inner” behavior at the ends of the flow channel is treated with a fine mesh in the longitudinal coordinate; a smoothly expanded mesh is sufficient for resolving the “outer” behavior in between. The grid is also selectively refined near the singularities in the convective coefficients. At unit Péclet number (based upon width of the flow channels) the resulting selectivity curves are found to be in remarkably close quantitative agreement with those for plug flow, despite major differences in the inner solute concentration profiles—a feature that does not persist at significantly higher Péclet numbers. Drawing an analogy with sedimentation-diffusion processes in rotating cylinders, the underlying mechanism of antipolarization is interpreted in terms of a circulation-flux parameter. In this way we illuminate the apparent robustness of the fractionation scheme with respect to details of the convective field.