A one-way valve and a flexible package including the valve are disclosed. The valve basically comprises a base member, a flexible septum and a stake. The base member is mounted on a wall of the package and includes a valve seat and at least one inlet port. The septum is formed of a resilient material and is connected to the base member by the stake, with a first portion of the septum contiguous with the stake fixed in position with respect to the base member and a second portion of the septum engaging the valve seat and covering and sealing the at least one inlet port. The septum is arranged to flex off of the valve seat to unseal the at least one inlet port when the pressure of gas at the at least one inlet port reaches a threshold.