The paper analyzes a microscopic regime of strain, different from the one conventionally considered, that presumably takes place in swollen polymers showing strong microscopic phase separation, such as ion-exchange resins in water. Such systems show linear dependence of the elastic pressure on swelling in contrast to the Flory-Rehner theory and its modifications. The present work proposes a simple model that predicts this kind of behavior. Swelling is considered as a non-affine 'inflation' of the hydrophobic matrix by small aggregates of water molecules ('droplets') adsorbed by highly hydrophilic groups, whereas the macroscopic dimensions of the sample change as a result of the compression of the 'films' separating the droplets. This compression is then analyzed along the classical lines. In the case of the Dowex resins a partial test of the model based on the reported shear moduli showed reasonable agreement with experiment.