The vibration and buckling of the coating-FGM-substrate conical shells (CFGSCSs) with mixed boundary conditions (MBCs) under the hydrostatic pressure are studied. The basic equations of CFGSCSs are displayed based on the Donnell-type linear shell theory and solved using by Galerkin's method. The novelty of current study is to obtain formulas for the critical hydrostatic pressures (CHPs) and the cyclic frequencies (CFs) of CFGSCSs with the MBCs. Finally, the influences of FGM cores and variation of the material gradient index on the CFs and CHPs for CFGSCSs are studied.