The film thickness, flow regimes, and flooding points for the countercurrent annular flow of corn oil (Mazola) and carbon dioxide at 338 K and pressures between 7.6 and 20.6 MPa are examined experimentally. The film flows down a stainless steel rod with a diameter of 10 mm and a length of 1000 mm that is inserted in a glass tube with an internal diameter of 15 mm, yielding an annulus of 2.5 mm. The film thickness adheres to Nusselt's equation for smooth water films. With increasing liquid flow rate, the falling film exhibits the following flow regimes: wavy film, troughs/crests on the film, drop formation, and flooding. The countercurrent gas flow affects the flow regime of the liquid film. The flooding points for the falling film column can be correlated with the same equation as the flooding points for packed columns with various packings and fluids at different states (high and ambient pressure).