This article presents a method to study the buckling of freely-supported functionally graded (FG) truncated and complete conical shells under external pressures in the framework of the shear deformation theory (SDT). The basic relations, modified Donnell type stability and compatibility equations have been obtained on the basis of SDT. The material properties of truncated conical shells are functionally graded in the thickness direction according to a volume fraction power law distribution. To solve this problem is used an unknown parameter 2 in the approximation functions. One of innovations is to achieve closed-form solutions for critical lateral and hydrostatic pressures of freely-supported FG truncated and complete conical shells in the framework of the SDT. The parameter A which is included in the obtained expressions is get from the minimum conditions of critical external pressures. Finally, influences of shear stresses, volume fraction index and shell characteristics on the critical lateral and hydrostatic pressures are investigated. (C) 2015 Elsevier Ltd. All rights reserved.