The objective of this study was to develop kinetic model for the MBR and investigate kinetic characteristics of the gravitational flow transverse direction MBR system. Kinetic model was derived by mass balance of substratc and biomass combined with empirical membranc filtration rerm for the MBR. To find kinctic values, permeale flux and COD removal were analyzed through the laboratory, MBR operation as different solids retention times. Permeate flux was ranged 2.5-5.0 LMH (L/m$^2$/hr) as sludge characteristics in each run. Although the soluble COD in the bioreactor was changed, the effluent COD was stable as average 99% removal rate during the experimental periods. Y$_g$ of this MBR system was higher than those of cross-flow MBR processes. The kinetics of this MBR showed that smaller k, larger b, and larger K$_s$ values than the conventional activated sludge process. These results indicated that substrate was used for cell maintenance rather than growth in this MBR system.