In this study, the nonlinear dynamic buckling of functionally graded (FG) truncated conical shells subjected to axial compressive load varying as a linear function of time is investigated. The material properties of the FG truncated shell are assumed to vary continuously through the thickness of the shell. The nonlinear pre-buckling deformations of the FG truncated conical shell are taken into account. The fundamental relations and modified Donnell type nonlinear dynamic stability and compatibility equations of the FG truncated conical shell are derived and solved by using the Superposition principle, Galerkin and Runge-Kutta methods. The values of the dimensionless nonlinear critical time parameter have been found numerically. Finally, carrying out some computations, the effects of the compositional profiles, the variation of the truncated conical shell geometric parameters and the axial loading speed on the dimensionless linear and nonlinear critical time parameters have been studied. Comparing the results of this study with those in the literature validates the present analysis. (C) 2012 Elsevier Ltd. All rights reserved.