The aim of this work was to develop a modeling approach to solve the flow and oxygen transfer when the blood passes through the hollow-fiber membrane bundle. For this purpose, a "two-region" modeling approach was developed regarding the hollow fiber and blood regions. The oxygen transfer in these regions was defined with separate diffusion processes. Two dimensional single and multi-fiber geometries were created and flow solutions were obtained for a non-Newtonian fluid. The convection-diffusion-reaction equation was solved to produce the oxygen partial pressure distributions. As a benefit of coupling the interstitial flow field into the oxygen transfer through the hollow-fiber membrane bundle, the membrane resistance was taken into consideration. Thus, varying oxygen partial pressures were observed on the outer fiber surface, which is contrary to the common simplifying assumptions of negligible membrane resistance and uniform oxygen content on the fiber surface (Traditional approach). It was illustrated that, the current approach can be utilized to predict the mass transfer efficiencies without overestimating as compared to the predictions obtained with the traditional approach. Utilization of the current approach was found to be beneficial for the geometries with lower packing density which allows significant P(O2) variations on the fiber surfaces. For the geometries with dense packings, the above simplifying assumptions could be applicable. The model predictions were validated with the experimental measurements taken from a benchmark device.