A modified atmosphere packaging method creates a modified atmosphere in a package including an inner package and an outer package. The inner package is composed at least partially of a polymeric material substantially permeable to oxygen, while the outer package is composed of a polymeric material substantially impermeable to oxygen. After a food product such as raw meat is placed within the inner package, the inner package is flushed with a desired mixture of gases to substantially remove oxygen from the inner package. The flushed inner package is then sealed and inserted into the outer package without sealing the outer package. Next, the outer package is flushed with the desired mixture of gases to substantially remove oxygen from the outer package. After flushing the outer package, the outer package is sealed. An oxygen scavenger is provided in the package to substantially absorb any residual oxygen within the package. The oxygen scavenger is activated with an oxygen uptake accelerator to increase the rate at which the residual oxygen is absorbed.