The permeance of carbon dioxide, oxygen, nitrogen, and air through commercial polymers based on polyethylene (PE), biaxially oriented polypropylene (BOPP), and polyamide (PA) used for food packaging is reported. The influence of temperature (from 10 to 60 C) and crease stress cycles (30, 50, 70, and 110) on gas permeance is also analyzed. Generally, the highest changes in gas permeance changes with increased stress cycles are observed with films having a metallized layer in the structure, namely BOPPcoex/BOPPcoex.met and, to a lesser extent, BOPPcoex.met/PE laminate. The lowest crease stress influence on barrier properties is obtained for PE film. In this case, the highest activation energy for the permeability coefficient (P) is obtained. Normal progressions of activation energies for P are: N 2 ¼ Air4CO 2 4O 2 .