In this study, the thermoelastic buckling of functionally graded material (FGM) conical shells under nonlinear temperature rise across the thickness in the framework of the shear deformation theory (SDT) is investigated. To the derivation of basic equations is used modified Donnell-type shell theory. The Galerkin method is used to obtain the formula for non-linear buckling temperature difference of freely supported FGM truncated conical shell in the framework of the SDT. By changing the properties of FGMs and volume fraction index, the effect of transverse shear deformations on the non-linear buckling temperature difference is evaluated by comparing with the results of the classical shell theory (CST). Meanwhile, the effect of geometric parameters on the non-linear buckling temperature difference of the shear deformable FGM conical shells is discussed in detail. (C) 2016 Elsevier Ltd. All rights reserved.