The swelling processes of polymer gels are described by the diffusion equation for the displacement of a stretched polymer chain. This diffusion equation and its boundary condition are mathematically obtained from the stress-diffusion coupling model, which is a system of constitutive equations for polymer gels. Numerical analysis of the free swelling of a spherical and cylindrical polymer gels is carried out to show the change of the displacement of particles inside and the change in the radius of the gels with time, and the results of our calculation are compared with experimental data. The calculated results are in good agreement with experimental data.