In a previous article (part 1: Barenbrug, Th.M. A. O. M.; Smit, J. A. M.; Bedeaux, D. Macromolecules 1997, 30, 605) we used Monte Carlo methods to study the properties of lattice polyelectrolytes with fixed endpoints and proposed expressions for the conformational free energy of a single chain. By connecting these chains by means of tetrafunctional cross-links, a simple model network of lattice polyelectrolytes was conceived. Using the total free energy of the gel and the other constituents, we were able to predict equilibrium swelling (part 2. Barenbrug, Tn. M. A. O. M.; Bedeaux, D.; Smit, J. A. M, Macromolecules, preceding paper in this issue) under a variety of conditions with respect to the salt content and the linear charge density of the chains. The elastic behavior of the gel is described in this paper (part 3) in terms of the shear modulus as a function of the above conditions. We consider two well-defined swelling circumstances for the gel (cases 1 and 2) and compare our findings with recent experimental results.