This study describes the free-surface flow of a highly viscous liquid between two concentric cylinders. In the process the morphology of the phase boundary is determined using a straight volume of fluid approach. Due to large differences in viscosity the gaseous phase is considered as vacuum. The numerical results of free-surface flow measures are compared to previous calculations and experimental values. The investigation shows that the used two-phase method is well-suited to predict the location and shape of the interface.