Numerical simulation was carried out to elucidate the effects of gel-bead diameter, initial cell density, initial phenol concentration, and oxygen concentration in the bulk liquid on the change in the oxygen concentration profile in a gel bead during biological aerobic phenol degradation with activated sludge entrapped in the calcium alginate gel bead. The results of simulation show that oxygen-limiting occurs in the central parts of the gel beads under most conditions examined in this study. After phenol degradation starts, the oxygen concentration in the beads is found to be immediately reduced and slightly increased instantly, and then slowly decreased linearly to a minimum value as the degradation proceeds. Finally, the oxygen concentration rapidly recovers to the same level of the bulk liquid. For small-sized gel beads, at low initial cell densities no oxygen-limiting is found to occur even in the core of the gel beads due to the small mass transfer resistance for oxygen diffusion, low oxygen consumption rate, or both. The critical gel-bead diameter for freedom from oxygen depletion is about 1 mm. At high phenol concentrations, oxygen may penetrate to the central parts of the gel beads as a result of reduction of the oxygen consumption rate by substrate inhibition. The effectiveness factors for small-sized cell-loaded gel beads were found to be unity at relatively high phenol concentrations in the bulk liquid and to decrease with increasing cell density. Further, it is found that at higher initial cell densities or for large-sized gel beads a high cell density layer will be formed around the surface of the gel beads during phenol degradation periods.