The productivity of an immobilized cell biocatalyst is often limited by the amount of oxygen that reaches cells located at interior regions of the biocatalyst. These diffusive limitations depend on a multitude of factors including the oxygen supply, the cellular uptake kinetics, and the cell density of the material. Large cell densities, which are desired for high productivity, are also likely to reduce the percentage of cells that receive an adequate supply of oxygen. To develop a better understanding of how different conditions affect biocatalyst behavior, a computational model of immobilized hybridoma cells was developed. The model accounts for oxygen diffusion and consumption, cell proliferation and death, and monoclonal antibody production. This model assumes that cellular productivity is limited only by the supply of oxygen and that the growth media is continually replenished so that nutrient levels remain high and wastes are eliminated. Biocatalyst performance is evaluated by monitoring the amount of monoclonal antibody produced by the cells. Model predictions agree with experimental measurements reported in the literature and indicate that for long operation time the supply of oxygen, biocatalyst size, and cell kinetics have a significant effect on biocatalyst performance, whereas the initial cell loading has only a relatively small effect. Under typical culture conditions, we find that oxygen penetrates to a maximum depth of about 0.4 mm. Accordingly, cells immobilized farther than this threshold distance receive an insufficient supply of oxygen.