A study has been made to determine the critical time parameters of truncated conical shells with functionally graded coatings (FGCs) and subjected to a time dependent axial load in the large deformation. The method of solution utilizes Superposition principle and Galerkin procedure. Donnell-Karman type non-linear differential equations for the truncated conical shell with FGCs are derived and reduced to ordinary differential equation with the time dependent coefficient. The Runge-Kutta method and modified Budiansky-Roth criterion are then used to solve this non-linear differential equation with the time dependent coefficient. Finally, effects of compositional profiles of coatings, variation of truncated conical shell parameters and loading speed on the dimensionless linear and non-linear critical time parameters have been studied. Comparing the results of this study with those in the literature validates the present analysis. (C) 2013 Elsevier Ltd. All rights reserved.