Equations for the equilibrium between the stresses and the degree of swelling, and also for the mass balance of substrate and functional groups, are proposed in order to analyze the attachment of active species onto gelular polymer bead. The asymptotic expansion technique was used to solve these equations when the relaxation rate of polymer in solvent is higher than the reaction rate and the reaction rate is much faster than the diffusion rate. It was shown that the interaction between solvent and polymer with attachment can be explained from the simulation. The equations proposed can be utilized to better understand the control of active species distributions in the polymer bead.