Model systems of cross-linked polyelectrolyte gels were investigated by means of Monte Carlo simulations. The model contained a charged defect-free three-dimensional network of a diamond-like topology and explicit counterions. Pressure vs volume relations and chain extensions were determined and compared to those of the corresponding polyelectrolyte solution. The structure of the gel was characterized by radial distribution functions. In the swollen state, the network particles and the counterions are inhomogeneously distributed in space. Also, the properties of the polyelectrolyte gels were investigated at different charge density, cross-linking density, chain flexibility, and counterion valence. An increase in the gel volume was observed for increasing charge density, decreasing cross-linking density, and increasing chain stiffness. The exchange of the monovalent counterions for divalent counterions reduced the equilibrium volume of the gel substantially. The affine assumption, which states that a linear relation exists between chain end-to-end separation and macroscopic gel size, was found to be only of limited validity, whereas the Gaussian chain approximation was never fulfilled for polyelectrolyte gels.