A modified expression for the change in chemical potential of a solvent, in a polymer network, due to isotropic swelling was obtained by substituting a non-Gaussian chain length probability distribution in Flory’s statistical analysis of rubber elasticity. The affine non-Gaussian expression for the free energy change due to elastic deformation was compared to both the traditional Flory and the James Guth "phantom network" expressions for the free energy change due to elastic deformation using available experimental data for the swelling of highly cross-linked polymeric resins. Among the different models for the elastic contribution to the free energy change resulting from isotropic swelling, the non-Gaussian elasticity expression was found to be as good as, or slightly better than the Flory expression, and clearly superior to the James-Guth phantom network expression. Both of the two different expressions used to represent the free energy of mixing, the Flory-Huggins expression and a modified version of the quasi-chemical mixing expression, were found to be equally successful when describing the isotropic swelling of cross-linked polymeric resins.