The formulation and numerical investigation of free surface transport within a hollow glass ampule art presented. The glass ampule is treated as a vertical film with a finite pressure difference across the film. A modified form of the marker and cell method within a semi-implicit algorithm is used to deal with the free surface problem, and full consideration of surface tension and viscosity effects is taken into account. It is found that the viscous effects on the free surface pressure conditions can be neglected because of the dominance of the surface tension effects. Furthermore, it is found that the convective terms have less than 1% effect on either the pressure or the velocity fields. The results clearly show the effects of a pressure differential across the glass ampule. The movements of the inner and outer free surfaces and the corresponding pressure distributions at these surfaces are analyzed. An interesting phenomenon corresponding to the reversal of direction of the movement of the free surfaces is shown to be related to a reversal in direction of the pressure differential.