Time-dependent volume changes are important in polymer processing because the material is frequently cooled rapidly from a rubbery melt to a nonequilibrium glassy solid. The present work uses a generalized constitutive equation of the authors, in which time-dependent compressibility effects have been included. Its use is illustrated by two examples: (1) simultaneous pulling and cooling near the glass transition temperature, for which we present our own data; and (2) simulation of the packing and cooling steps in injection molding, for which we use literature data. Our experimental data, involving the pulling and cooling of fiber-like samples of polystyrene near T(g), were fit satisfactorily in all runs, although we note that there is considerable adjustability in a key function (the modulus-temperature relation). This example illustrates clearly the need to couple the mechanical and thermal effects in the theoretical formulation. In a separate analysis the packing and cooling steps in injection molding were simulated (by making certain simplifications in the temperature profiles) and compared with literature data.