A vibratory pumping machine including a pumping chamber disposed within a housing for the machine having an inlet tube that is insertable into a container having a liquid therein to withdraw the liquid from the container upon actuation of the pumping mechanism also located within the housing. The chamber includes an oscillating rod that engages a resilient outlet member to form a vacuum within the chamber which draws the liquid upwardly through the tube into the chamber for dispensing through the outlet member. A mechanism including the pumping chamber can be utilized to withdraw liquids from within container of various shapes and sizes, as well as to introduce other fluids, such as gases, into containers containing such liquids.