Thermo-rheologically / piezo-theologically simple viscoelastic constitutive equations are adopted for the material behavior of a generic polystyrene, in both the deviatoric and dilatational domains, in order to investigate the effect of density relaxation on the development of the thermal residual stresses in a thin injection-molded strip. A preliminary study is undertaken to assess the ability of the proposed dilatational viscoelastic constitutive equations to capture some of the density-relaxation behavior such as the isobaric volume relaxation following a sudden quench from above the glass-transition temperature and upon constant rates of cooling at different temperatures and pressures. In this preliminary study, different combinations of relaxation functions and shift factors are investigated. An appropriate combination is selected and used for the residual-stress analysis. The numerical simulation of the development of the stresses in a one-dimensional cavity qualitatively predicts the correct stress profile across the thickness of the molded part, as well as the dependency of this profile on some of the material properties and molding conditions. In general, the investigation presented in this paper suggests that density relaxation plays an important role in the development of residual stresses in molded parts.