This paper reports the results of an investigation into the stability of an individual multi-walled carbon nanotube subjected to combined bending and axial compression loading. The effect of van der Waals forces between two adjacent tubes is taken into account and a multiple-shell model is adopted. According to the ratio of radius to thickness, multi-wall carbon nanotubes discussed here are classified into three cases: thin, thick, and nearly solid. The critical combined loading and the stability mode are calculated for various ratios of radius to thickness. Results carried out show that the stability mode corresponding to the critical combined loading is unique, which is obviously different from the purely axial compression buckling of an individual multi-wall carbon nanotube. It is also seen from numerical examples that the distribution of the maximum critical bending stresses applied on each tube of MWNTs under combined bending and axial compression loading is dependent on the ratio of radius to thickness and the ratio of axial compression loading to bending moment. The new features of the combined stability of multi-walled carbon nanotubes under combined bending and axial compression loading and some meaningful and interesting results in this paper are helpful for the application and the design of nanostructures in which multi-wall carbon nanotubes act as basic elements.