The present disclosure provides a container storage system (100) including base tray (20) with a flat platform (22) having a polygonal shape and an array of spaced-apart holes, (24) the flat platform (22) defining a perimeter edge (26). The base tray also includes a substrate (28) beneath the flat platform. The substrate defines a peripheral edge (30) and a sidewall (32) extends upward from the peripheral edge. A plurality of flexible containers (300) are on the flat platform. Each flexible container has four panels, the four panels forming a body portion (304), a neck portion (306) with a closure (308), and a tapered transition portion (310) between the body portion and the neck portion. Each flexible container is inverted such that the neck portion extends downward through a respective hole and the tapered transition portion contacts the flat platform to support the inverted flexible container. One panel (302) of at least one inverted flexible container contacts a panel of another inverted flexible container.