Non-durable self-supporting flexible containers having product volumes and structural support frames are provided with vents to facilitate equalization of the pressure inside the product volume to the pressure of the environment outside of the containers. The vents enable rapid recovery of the structural support from a deformed state, which occurs when a fluent product is dispensed, to an undeformed state. For this purpose, the vents comprise vent paths between the environment outside of the containers and the product volume. The vents may further comprise a non-wetting material surrounding the entrance and exit of the vent path and/or microtexturing or a spacer to maintain space for air flow in the vent path.