In certain real situations, polymer networks cannot swell freely but are subjected to constraints by action of external forces or geometric restrictions. In this contribution, the restriction to swelling by adhesion of a cross-linked polymer film deposited on a rigid substrate is considered. Such constraints prevent swelling in plane, and the osmotic force concentrates on extension of network chains in the direction normal to the surface. We analyze existing rubber elasticity models taking into account finite extensibility of network chains and derive the elastic contribution to the chemical potential of the solvent in swollen networks. For the mixing contribution to the change of the Gibbs energy, it is more appropriate to consider the network containing cross-links, but with undeformed network chains than an un-cross-linked polymer of infinite degree of polymerization, because continuing formation of bonds within an infinite molecule further decreases the entropy. The additional term is proportional to ...