A rotary packing apparatus wherein a plurality of bag-support elements support a flexible bag in suspension. The support elements are moved intermittently along an endless circular path, and the bags are fed to the bag-support elements on the path. Thereafter, objects are placed in the bags at a given position on the path. The filled bag is then subjected to a vacuum and sealed. Two vacuum chambers are provided between the position at which objects are placed in the bags and the position for sealing the bags, such that the bags are subjected to a vacuum at each of the two vacuum chamber stages, and are exposed to atmospheric pressure between these two stages.