The linear vibrations of sandwich cylindrical shells with flexible honeycomb core and nanocomposite face sheets are studied numerically. The vibrations of single-layer nanocomposite cylindrical shell are considered too. The flexible honeycomb is produced by fussed deposition modeling additive technology. Nanocomposite layers are reinforced by carbon nanotubes. The faces sheets and honeycomb core displacements projections are expanded up to the quadratic terms and cubic terms with respect to transverse coordinates, respectively. Following Reddy higher order shear theory, the displacements projections of single-layer nanocomposite cylindrical shell are expanded up to quadratic terms. The Rayleigh – Ritz method is applied to analyze linear vibrations of sandwich cylindrical shell and single-layer nanocomposite cylindrical shell. The effect of reinforcement of nanocomposites by carbon nanotubes on structure eigenfrequencies is studied.