In this study, the stability of sandwich conical shells covered by functionally graded and uniform distributed carbon nanotube-reinforced composite coatings under external pressures is carried out. The mechanical properties of the carbon nanotube and matrix are assumed to be graded through the thickness of the coatings via three types of grading rule. The basic relationships and stability equations of sandwich conical shells reinforced by carbon nanotubes are obtained employing the modified Donnell-type shell theory and generalized first-order shear deformation theory. The Galerkin procedure is employed to define expressions for the external buckling pressures. For the accuracy of the proposed formulation, the results are compared with the results that are published in the literature. It follows a systematic study aimed at checking the sensitivity of the structural response to the type of pattern and the volume fraction of carbon nanotubes in the composite coatings.