In this study, mechanical buckling of composite cylindrical panels reinforced with single walled carbon nanotubes under axial compression is investigated. Distribution of SWCNTs across the thickness of the panel is considered to be uniform or functionally graded. Mechanical Properties of the carbon nanotube reinforced cylindrical panel are obtained using micromechanical approaches such as the modified rule of mixtures and Eshelby-Mori-Tanaka approaches. The governing equations are obtained by using Hamilton’s principle based on first-order shear deformation theory and considering strain-displacement linear relation. An energy based Ritz method and Chebyshev polynomials are used to obtain the critical buckling load of composite cylindrical panels. In addition, the effect of various parameters such as boundary conditions, geometrical conditions, distribution pattern across the thickness of carbon nanotubes and their volume fraction are studied on the critical buckling load. It is shown that, FG-X pattern of SWCNTs distribution results in the maximum critical buckling load and by increasing the volume fraction of carbon nanotubes, the critical buckling load of composite cylindrical panel increases.