The swelling of regular, tightly meshed model networks is investigated by a molecular-dynamics-Monte Carlo hybrid technique. The chemical equilibrium between two simulation boxes representing the gel phase and a solvent bath, respectively, is obtained by subjecting the Lennard-Jones particles of a binary mixture, serving as explicit solvent, to the particle transfer step of Gibbs ensemble-Monte Carlo. The swelling behavior, especially preferential absorption of a single component, whose dependence on temperature, pressure, and fluid composition is studied, also depends significantly on the size of the central simulation cell. These finite-size effects correlate well with those exhibited by the density of solvent-free (dry) networks. A theoretical expression, whose derivation is based on network elasticity (of dry networks) yields finite-size scaling behavior in good accord with simulation results for both dry networks and gels in contact with solvent baths. This expression can be used to extrapolate the swelling behavior of simulated finite systems to infinite system size.