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. A valve cover is mounted on the valve body, and includes an axially-extending portion formed of an elastic material overlying the valve seat and covering a substantial axially-extending portion thereof. The valve portion defines a predetermined radial thickness and forms an interference fit with the valve seat. The valve portion and the valve seat define an axially-extending seam therebetween forming a normally closed, axially-extending valve opening, and 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 connect the valve opening in fluid communication with the at least one flow aperture and thereby allow the passage of substance from the variable-volume storage chamber through the valve opening.