A flexible pouch defining a variable volume storage chamber and one-way valve assembly for aseptically storing a substance, dispensing multiple portions of the stored substance therefrom in cooperation with a pump, and maintaining substance remaining in the pouch in an aseptic condition sealed with respect to ambient atmosphere. The one-way valve includes a valve seat and elastic valve cover portion overlying the valve seat forming an interference fit therewith defining a normally-closed seam therebetween. The valve portion is movable radially between (i) a normally closed position with the valve portion engaging the valve seat, and (ii) an open position with at least a segment of the valve portion spaced radially away from the valve seat to allow substance from the storage chamber through the valve opening. The one-way valve maintains substance remaining in the variable-volume storage chamber in an aseptic condition sealed with respect to the ambient atmosphere.