A gravity feed shelving system is provided in which specially configured tiers contain necked-down channels for the receiving, storing and dispensing of series of flexible packages such as flex bags. Each channel is configured with relatively wide receiving and dispensing portions at the rear and front of the tier, respectively, and a narrowed intermediate portion that partially compresses the flex bags and restrains them against their removal from the channel until the flex bag passes from the intermediate portion into the dispensing portion. The tier has an operatively sloped orientation so that, once placed within the receiving portion of the channel, each flex bag is urged along the channel and into the intermediate portion by the force of its own weight.