In this paper, a study is conducted on the free vibrational analysis of a cylindrical sandwich shell with a re-entrant auxetic honeycomb (AH) core made of ceramic-metal functionally graded material (FGM). The volume fraction (mass fraction) of ceramic in the functionally graded auxetic honeycomb (FGAH) core varies from zero at the inner surface to one at the outer one based on a power-law function. It is supposed that the core is covered with a homogenous inner layer made of metal and a homogenous outer one made of ceramic. The first-order shear deformation theory (FSDT) is hired and the shell is modeled mathematically. The governing equations are attained via Hamilton’s principle, and an analytical solution is presented for a simply supported shell via the Navier method. The impacts of several parameters on the natural frequencies are inspected including the power-law index (material gradation in the core), the thickness of the core-to-thickness of the shell ratio, the thickness-to-radius ratio of the shell, and geometric factors of the re-entrant cells (inclined angle, aspect ratio, and thickness of the walls). It is discovered that the natural frequencies decrease by growing the inclined angle in the FGAH core. It is concluded that for each vibrational mode, there is an optimal ratio between the values of the thickness of the core and the thickness of the shell which leads to the highest natural frequency. Manuscript profile