A finite-strain theory for the study of the overall behavior of polymeric gels containing microvoids is presented. The swollen porous polymeric gel is modeled as a two-component body composed of two incompressible materials, namely, an elastic porous polymer imbibed with a solvent. The chemical equilibrium is assumed to be preponderate at the interface between the porous polymer and its environment where the chemical potential of the solvent is fixed. The initially dry porous polymer undergoes large deformations induced by absorption of a solvent from the environment and mechanical loading. In this paper an attempt is made toward obtaining an estimation of the macroscopic responses of the swollen porous polymer to prescribed proportional loadings. To this end, a two-level representation of the material at hand for which the Representative Volume Element (RVE) imbibed with a solvent is a simple axisymmetric cylinder composed of a homogeneous matrix surrounding a spherical void, is considered. The numerical study addresses the situation where the RVE is subjected to prescribed axial and lateral overall stresses under conditions of constant overall stress triaxiality. For fixed values of the Flory-Huggins parameter and nominal concentration of the solvent, the overall stress-strain behavior of the RVE model, the influence of the initial porosity, and the prescribed stress triaxiality ratio have been obtained.