The transport process of oxygen and other gas species across red blood cell (RBC) membrane is of great importance for better understanding the critical biological functions of RBCs, and the stopped-flow experiments have often been employed for such investigations. In previous stopped-flow analyses, the RBC had usually been represented by a spherical capsule based on the RBC volume, and an assumed unstirred layer (USL) thickness had been used to determine the membrane permeability. In this research, unlike these previous studies, we simulate the oxygen uptake process with different RBC shapes (shperical, ellipsoidal and biconcave) and examine the effects of USL thickness and membrane permeability over broad ranges based on literature values. Our results show that the excess membrane area can greatly improve the oxygen transport efficiency, and a same uptake half-time can be obtained using different combinations of USL thickness and membrane permeability. These findings raise concerns on the reliability and uncertainty for the results and conclusions in previous studies, and also call for more complete numerical models, for example, with the fluid flow and cell deformation considered, and more in-depth investigations on the oxygen transport processes.