This paper describes the transport process, rejection curve and molecular weight cut-off (MWCO) of ultrafiltration membranes by using a log-normal distribution, Poiseuille flow and steric interaction between solute molecules and pores. The rejection coefficient of membranes was expressed with an analytical function of D*/a (the ratio of geometric mean diameter to solute diameter) and sigma (geometric standard deviation). For ultrafiltration membranes with different MWCO, the pore size distribution can be divided into three zones by a: Zone 1, long tail-effect of big pores (sigma > 1.55); Zone II, linearization of pore size distribution parameters (D*, sigma) (1.15 < sigma < 1.55); Zone III, sieving effect (1 <= sigma < 1. 15). The relationship between D*/D-MWCO (D-MWCO is the diameter of solute molecule at R = 0.9) and sigma was described by the Extreme model: D*/(DMWCO) = A e((-e(-z)-z+1)), z = sigma-1/w (sigma is an element of[1,infinity]), A = 1.296, w = 0.299 For any rejection coefficient, the relationship between D*/a and sigma can also be described using the Extreme model. A method to predict the pore size distribution and MWCO of ultrafiltration membranes by two points was first presented and verified by hollow fiber membranes spun at different shear rates. The shear rate in the spinning of hollow fiber membranes dominated the pore size distribution parameters (D*, sigma), which played an important role in membrane performance. With an increase in shear rate, the geometric standard deviation (sigma) was strongly suppressed, which resulted in hollow fiber membranes with low MWCO. (c) 2006 Elsevier B.V. All rights reserved.