Membrane bioreactors (MBRs) are becoming more suitable alternatives for conventional wastewater treatment devices. The performance of a pressure-driven MBR is dominantly affected by the hydrodynamic conditions of the system. This study was conducted to investigate various hydrodynamic characteristics including shear stress, cross-flow velocity, and membrane fouling resistance, using computational fluid dynamics (CFD). Simulation of two- and three-phase flow for a flat-sheet submerged membrane module was carried out, and the results were compared with the experimental data. The CFD simulation was implemented to analyze the fluid-flow pattern, shear stress on membrane surfaces, and cross-flow velocity between membranes at various mixed liquor suspended solid concentrations in the bioreactor. It was shown that the cross-flow velocity plays an important role in the membrane fouling and determination of the critical particle diameter. To achieve an optimal operating condition, the critical particle diameter was calculated at different air flow rates and permeate fluxes. The CFD results showed that the outermost membranes are more prone to fouling because of the lower shear stress on their surface as well as the lower cross-flow velocity between them and the module wall. Moreover, the effect of the air bubble diameter on the air and liquid shear stress was investigated to determine an optimal bubble size.