In this work, the stability of conical shells made of functionally graded materials (FGMs) subject to a uniform external pressure, which is a power function of time, has been studied. The material properties of functionally graded shells are assumed to vary continuously through his thickness of the shell, according to a power law distribution of the volume fractions of the constituents. The fundamental relations, the dynamic stability and compatibility equations of functionally graded truncated conical shells are obtained first. Applying Galerkin's method, these equations have been transformed to a pair of time dependent differential equation with variable coefficient. This differential equation is solved for different initial conditions by variational method by using Lagrange-Hamilton type principle. Thus, general formulas have been obtained for the critical parameters. The results show that the critical parameters are affected by the configurations of the constituent materials, loading parameters variations, the variation of the semi-vertex angle and the power of time in the external pressure expression variations. Comparing results with those in the literature validates the present analysis. (C) 2004 Elsevier Ltd. All rights reserved.