A full understanding of the elastic properties of hydrogels under swelling is required for their practical application in the chemical and biomedical engineering fields. This is because hydrogels are expected to retain water during mechanical use in moist atmospheres. In the present study, we investigated the relationship between the elastic modulus and the swelling ratio in a specific type of hydrogel (a polyacrylamide gel). The elasticity and swelling data revealed that these two parameters are proportionally related in hydrogels comprising adequate amounts of monomers and crosslinkers. We also demonstrated that this proportional relationship inherently conforms to the linear elastic behaviour predicted by the Flory-Rehner free energy function (the F-R model). The implicit rule is established by the extended F-R model with two scaling exponents. The extended model is capable of representing the irregular elasticity of swollen gels formed from low- or high-molecular-weight polymers.