Abstract This work analyses the natural frequencies of composite conical panels made of a polymeric matrix reinforced with uniform or functionally graded carbon nanotubes (FG-CNTs). The mechanical properties of the composite conical panels rely on a refined rule of mixtures, including some efficiency parameters, whereas the kinematics of the problem is here tackled with the first order shear deformation shell theory (FSDT) and the Donnell’s theory. The expressions of the virtual strain and kinetic energies of the conical panels are substituted into the Hamilton’s principle. A matrix formulation of the free vibration problem is achieved using the conventional Ritz method, with the shape functions stemming from the Gram-Schmidt process. Based on a parametric investigation, we assess the key role of the CNT volume fractions and patterns, and check for their effect on the free vibrations of the composite conical panels, as useful for practical applications.