In this study, the vibration and buckling of functionally graded (FG) orthotropic cylindrical shells under external pressures is investigated using the shear deformation shell theory (SDST). The basic equations of shear deformable FG orthotropic cylindrical shells are derived using Donnell shell theory and solved using the Galerkin method. Parametric studies are made to investigate effects of shear deformation, orthotropy, compositional profiles and shell characteristics on the dimensionless frequency parameter and critical external pressures. Some comparisons among various theories have been performed in order to show the differences between the parabolic shear deformation theory (PSDT) and several higher-order shear deformation theories (HSDTs). (C) 2014 Elsevier Ltd. All rights reserved.