An elastomeric gel is a cross–linked polymer network swollen by a solvent. Computational models of gels need to resolve the strong coupling between the diffusion of the solvent and the deformation of the elastic network. We present here a continuum mechanics model to describe the gel deformation and the coupled fluid permeation in the polymeric network, and the first results we have obtained with it. These consist of numerical simulations of two basic experiments: the free swelling deformation of a dry specimen and an indentation test performed on a swollen sample.