Chemically crosslinked polyelectrolyte networks are known to exhibit discontinuous volume phase transitions, the onset of which may be caused by a number of factors, most notably the solvent quality and the ionic environment of the network. We have previously shown through molecular dynamics simulations that, for chemically crosslinked polyelectrolyte networks in equilibrium with a pure solvent, the interplay between the counterion excluded-volume entropy and the electrostatic energy--factors not explicitly considered in the classical Flory-Tanaka model--appears to have an important role in driving these phase transitions [Yin et al., J. Chem. Phys. 123(17):174909, 2005]. In our current work we use a combination of Monte Carlo and molecular dynamics techniques to simulate chemically crosslinked polyelectrolyte networks in equilibrium with salt solutions. These simulations are performed in the osmotic ensemble: The amount of crosslinked polyelectrolyte is fixed and the system is isothermal, while the chemical potential of the salt ions and the osmotic pressure of the system are set to equal those of the external salt solution reservoir, thus allowing fluctuations both in the concentration of absorbed salt and in the volume of the system. Using this approach, we examine how factors such as the salt concentration and the exchange of monovalent and divalent counterion influence the volumetric behavior of chemically crosslinked polyelectrolyte networks. The simulations allow us to study the absorption, condensation, and diffusion of ions in the network, and can also be extended to model the complexation and partitioning of noncrosslinked polyelectrolytes in chemically crosslinked polyelectrolyte networks. We present the simulation results as they relate to the Flory-Tanaka theory and to experiments performed near physiological conditions.