This paper discusses an approach to incorporate density and temperature terms in the well-known stretched exponential (SE) model for predicting the stress relaxation behavior of polymer foams. We have developed this approach for closed-cell polyurethane foams (PUFs) and verified using experimental data for accuracy. The SE model was first examined using short-term experimental data to predict long-term stress relaxation behavior of PU solid (PUS). The corresponding model parameters were then extracted for PUS and two PUFs with different densities (PU404 and PU415) at three different test temperatures. Finally, an expression was developed in conjunction with the modified Gibson–Ashby relationship and the Arrhenius equation and validated for other foam density (PU420) and test temperatures. The predictions were found to be reasonably good with more than 90% accuracy.