According to the framework of the Donnell's shell theory the stability behavior of functionally graded (FG) truncated conical shell interacting with two-parameter elastic foundations within the shear deformation theory (SDT) is investigated. The major goal of this research was to obtain a closed form of the solution for critical external pressures associated with the problem outlined above. The basic equations of FG truncated conical shell shells subjected to the external pressures are derived within the SDT. By using the Galerkin method to resulting basic equations are obtained the expressions for critical hydrostatic and lateral pressures of FG truncated conical shell interacting with two-parameter elastic foundations within the SDT. In particular, similar expressions within the classical shell theory (CST) are obtained, also. Comparison the current results and those available in the literature demonstrates the availability and accuracy of solutions. Finally, the calculation and presentation of the effects of many parameters included in the analysis conclude the goals to be reached in the study. (C) 2016 Elsevier Ltd. All rights reserved.