We use hybrid molecular dynamics/Monte Carlo simulations and coarse-grained polymer models to study the swelling of polyelectrolyte gels in salt solutions. Besides existing industrial applications, such gels have been recently proposed as a promising agent for water desalination. We employ the semi-grand canonical ensemble to investigate partitioning of the salt between the bulk solution and the gel and the salt-induced deswelling of the gels under free swelling equilibrium and under compression. We compare our findings to the analytic model of Katchalsky and Michaeli which explicitly accounts for electrostatic effects. The partitioning of small ions predicted by the model well captures the deviations from the simple Donnan approximation observed in the simulation data. In contrast, the original model highly overestimates the gel swelling, predicting even chain stretching beyond contour length. With a modified model, where we replace the Gaussian elasticity with the Langevin function for finite extensibility, we obtain nearly quantitative agreement between theory and simulations both for the swelling ratio and for the partitioning of salt, across the whole range of studied gel parameters and salt concentrations. The modified model thus provides a very good description of swelling of polyelectrolyte gels in salt solutions and can be used for theoretical predictions of water desalination using hydrogels. These predictions are much less computationally demanding than the simulations which we used to validate the model.