The buckling analysis of annular composite plates reinforced by carbon nanotubes subjected to compressive and torsional loads are studied in this paper. The Mori-Tanaka method is employed to calculate the effective elastic modulus of composites having aligned oriented straight CNTs. The effects of CNTs volume fractions, orientation angles, boundary conditions and geometric ratio of plate are discussed. The results are calculated by analytical method based on classical plate theory and FE methods using ANSYS software and third order shear deformation theory for moderately thick laminated plates. It is found that the stability of plate increases as the thickness or inner to outer ratio rises and when the CNTs arranged in the circumferential direction the highest buckling load is achieved.