This paper presents results of an experimental study on the buckling of circular cylindrical shells loaded simultaneously with a bending moment and a compressive force. A high precision loading apparatus was designed, by which both the torque and the axial compression can be applied equally on both ends of the cylinder, so that the state of the bending under axial compression is established in the cylinder. Test specimens were made from polyester films, which had length-to-diameter ratios of 2, 5 and 10 and a diameter-to-thickness ratio of 300. In the experiment, the axial force was applied to induce axial stress varying in the range from 0 to 50% of the classical buckling stress. It has been shown that the buckling occurs when the bending stress added to the compressive stress approaches to the classical buckling stress. The experimental buckling stresses were compared with theoretical ones obtained by solving Budiansky's non-linear shell equations numerically.