Based on the first-order shear deformation and Donnell's shell theory with von Karman non-linearity, one decoupled stability equation for buckling analysis of functionally graded (FG) and multilayered cylindrical shells with transversely isotropic layers subjected to various cases of combined thermo-mechanical loadings is developed. To this end, the equilibrium equations are uncoupled in terms of the transverse deflection, the force function and a new potential function. Using the adjacent equilibrium method, one decoupled stability equation which is an eighth-order differential equation in terms of transverse deflection is obtained and conveniently solved to present analytical expressions for buckling loads of cylindrical shells under any type of loading. These analytical expressions can be used in design and as a benchmark in numerical studies. For numerical purpose, the formulation is applied to FG shells, a three-layer shell laminated of transversely isotropic layers, and sandwich shells with an isogrid lattice core and transversely isotropic face sheets. The results are validated with the existing ones in the literature. Finally, the effect of different parameters on the buckling loads in the presence of combined loadings is discussed in detail. Numerical results show that the existence of an initial hoop stress as a main type of initial imperfection has significant influence on the buckling behavior (including buckling values and mode shapes) of long cylindrical shells subjected to axial loading and this effect reduces for cylindrical shells with a lattice core. Furthermore, the critical values of torsion significantly reduce under combined loading. © 2018 Elsevier Ltd