The filtration behavior of submerged hollow fiber membranes with constant permeate flow operational mode was modeled on two different conditions: the maximum initial flux along the fiber is smaller than the critical flux (J(imax) < J(cr)); the maximum initial flux along the fiber is greater than the critical flux, but the averaged imposed flux is smaller than the critical flux Q(imax) > J(cr) but J(mi) < J(cr). When the maximum initial flux along the fiber is lower than the critical flux, no particle deposition occurs and the flux distribution can be characterized by a dimensionless parameter xi = 4LR(i)(-3/2)R(m)(-1/2). On the other hand, for J(mi) < J(cr) and J(imax) > J(cr), a steady state can be achieved after some initial deposition. The theoretical model shows that the filtration resistance caused by the initial deposition can be affected by J(mi)/J(cr) and fiber characteristics (L, R-i and R-m) and becomes significant for narrow and long fibers with a high J(mi)/J(cr). The models were also used to determine the optimal fiber length and radius for the submerged hollow fiber module. The simulation suggests that the optimal fiber lumen radius for fiber lengths of 0.5-3 m is 0.2-0.35 mm. These results should be relevant to the design of submerged hollow fiber modules.