Abstract: A plastic bag having a venting structure therein including flexible plastic front and rear walls sealed along their side edges and a venting sealing arrangement at one end of the walls including elongated spaced heat-sealed portions having puckers formed therebetween and unsealed openings proximate the sealed portions to permit pressurized gases from within the bag to pass through the unsealed openings and the puckered portions to the atmosphere, the puckered portions normally maintaining the portions of the side walls which form the puckers in contiguous contacting engagement to function as normally closed valves which prevent atmospheric air from entering the bag. The bag may have one or both walls fabricated from polyethylene containing ethyl vinyl acetate which permits the bag to have controlled breathing to permit oxygen to enter the bag at a controlled rate to maintain freshness of the product.