Laminar boundary-layer theory was used to quantify concentration polarization in ultrafiltration systems in which the membrane forms the base of a stirred cylindrical container: The flow was approximated as a rigid-body rotation above a stationary surface (Bodewadt flow), with a filtration velocity dependent on the osmotic pressure of the retained solute, and therefore varying with radial position on the surface. Because the analysis was limited to moderate solute concentrations and filtrate velocities, physical properties were assumed to be constant. The axisymmetric convective-diffusion problem was solved by a finite difference method. Boundary-layer results were compared with predictions based on the common assumption of a uniform stagnant film and with a hybrid approach of applying locally the stagnant-film relationships but allowing the film thickness to vary with position. In general, both of the approximate models under estimated polarization effects, with the hybrid approach yielding smaller errors. rn one set of simulations on the osmotic reduction in filtration rate caused by a completely retained solute, predicted errors in filtration rates with the models were moderate, with a maximum discrepancy of 21% (for the stagnant-film model). In the second set of simulations concerning polarization effects on apparent sieving coefficients for permeable solutes, the error in the predicted ratio of true-to-observed sieving coefficient was as much as 78% with the stagnant-film approach, while with the hybrid, model it was no more than 15%. Thus, the stagnant-film approach was much less satisfactory for inferring sieving coefficients than for predicting mean filtrate velocities. The predictive capability of the boundary-layer model was tested using previous filtration data for bovine serum albumin in two ultrafiltration cells. The agreement was excellent, provided that an appropriate value was selected for the angular velocity of the bulk fluid.