Microfluidic devices have been widely used for biological and cellular studies. Microbioreactors for three-dimensional (3D) multicellular spheroid culture are now considered as the next generation in in vitro diagnostic tools. The feasibility of using 3D cell aggregates to form multicellular spheroids in a microbioreactor with U-shaped barriers has been demonstrated experimentally. A barrier array is an alternative to commonly used microwell traps. The present study investigates oxygen and glucose concentration distributions as key parameters in a U-shaped array microbioreactor using finite element simulation. The effect of spheroid diameter, inlet concentration and flow rate of the medium are systematically studied. In all cases, the channel walls are considered to be permeable to oxygen. Necrotic and hypoxic or quiescent regions corresponding to both oxygen and glucose concentration distributions are identified for various conditions. The results show that the entire quiescent and necrotic regions become larger with increasing spheroid diameter and decreasing inlet and wall concentration. The shear stress (0.5–9 mPa) imposed on the spheroid surface by the fluid flow was compared with the critical values to predict possible damage to the cells. Finally, optimum range of medium inlet concentration (0.13–0.2 mM for oxygen and 3–11 mM for glucose) and flow rate (5–20 μL/min) are found to form the largest possible multicellular spheroid (500 μm), without any quiescent and necrotic regions with an acceptable shear stress. The effect of cell-trap types on the oxygen and glucose concentration inside the spheroid was also investigated. The levels of oxygen and glucose concentration for the microwell are much lower than those for the other two traps. The U-shaped barrier created with microposts allows for a continuous flow of culture medium, and so improves the glucose concentration compared to that in the integrated U-shaped barrier. Oxygen concentration for both types of U-shaped barriers is nearly the same. Due to the advantage of using U-shaped barriers to culture multicellular spheroids, the results of this paper can help to choose the experimental and design parameters of the microbioreactor.