The solidification of a molten layer of amorphous thermoplastic between cooled parallel plates is used to model the mechanics of part shrinkage and the buildup of residual stresses in the injection-molding process. Flow effects are neglected, and a thermorheologically simple thermoviscoelastic material model is assumed. The model allows material to be added to fill the space created by the pressure applied during solidification, so that this model can be used to assess packing-pressure effects in injection molding. The interactions between the mold surfaces and the solidifying material are accounted for by modeling different types of constraints through different model boundary conditions. For several sets of boundary conditions, parametric results are presented on the effects of the packing pressure--the pressure applied during solidification to counteract the effects of volumetric shrinkage of the thermoplastic--on the in-plane and through-thickness shrinkages, and on residual stresses in plaque-like geometries. Plaques that can shrink in the in-plane direction while in the mold are shown to shrink more and to have higher residual stresses than plaques that are fully constrained while in the mold. Although the results are presented in terms of normalized variables based on the properties of bisphenol-A polycarbonate, they can be interpreted for other amorphous thermoplastics such as modified polyphenylene oxide, polyetherimide, and acrylonitrile-butadiene-styrene.