A flexible pouch and valve assembly is provided for aseptically storing a substance, dispensing multiple portions of the stored substance therefrom, and maintaining substance remaining in the pouch in an aseptic condition sealed with respect to ambient atmosphere. The flexible pouch and valve assembly are receivable within a relatively rigid housing, and are adapted to cooperate with a pump for pumping discrete portions of substance from the pouch and through the one-way valve to dispense the substance therefrom. The assembly comprises a flexible pouch defining therein a variable-volume storage chamber sealed with respect to the ambient atmosphere for aseptically storing therein multiple portions of the substance. A one-way valve of the assembly includes a valve body defining an axially-extending valve seat and at least one flow aperture extending through the valve body and/or the valve seat.