A polymer network swells once it is in contact with a solvent. A gel phase forms after diffusion of solvent molecules inside the polymer due to chemical potential. Following the approach of Flory a specific functional form of free energy is defined, by considering to the deformation gradient of the network and solvent concentration as the two independent variables. Material point method (MPM) is used to numerically calculate the large elastic deformation of the network, and also a numerical method has been applied to calculate the free energy of mixing which is a function of solvent concentration. Finally the principal stresses can be obtained from the total free energy of the hydrogel. Key words: Swelling of polymers, Free energy function, large deformation analysis, Material point method