The stability of aqueous foams with polymer additives has been studied at different generation pressures. While the stability increases significantly with the increase of generation pressure for foams without any additive, it, however, changes weakly with the change in generation pressure for foams with polymer additives. Consistent with the previously reported studies, it is found that the foam stability (drainage half-life) increases, primarily due to the decrease of bubble size, at higher generation pressures, when the foam is produced in a packed bed. Calculations of drainage half-life were conducted using a modified lamella drainage model as well as a simple network model. It is found that the network model predictions agree reasonably well with measurements.