An annular reactor packed with matrices in which the catalysts/enzyme/microorganisms are immobilized, has been simulated and the results indicate that the overall resistance and hence the conversion depend upon the Thiele modulus and another parameter, a. This parameter characterizes the ratios of the diffusion times and die ratios of length scales of the bulk liquid phase and the solid phase in the reactor shell. Analytical solutions can be obtained for linear reactions and a simplified semi-analytic method has been used for obtaining concentration profiles for nonlinear reactions.