This paper examines the stability of thin three-layered truncated conical shells containing a functionally graded (FG) layer subjected to non-Uniform lateral pressure varying with the longitudinal coordinate. The material properties of the functionally graded layer are assumed to vary continuously through the thickness of the shell, and the variation of properties follows an arbitrary distribution in terms of the volume fractions of the constituents. Further, the fundamental relations for stability and compatibility equations of three-layered truncated conical shells containing an FGM layer have been obtained. These equations, ascertained via Galerkin's method, have been transformed into a pair of time-depen dent differential equations. Then, critical non-uniform lateral pressure has been Conclusively obtained. This paper is the result of a detailed parametric study conducted to determine the influences of thickness variations in the FG layer, radius-to-thickness ratio, lengths-to-radius ratio, and the material composition and material profile index on the critical parameters of three-layered, truncated, conical shells. Finally, the results will be validated through the comparison of obtained values with those in the existing literature. (c) 2007 Published by Elsevier Ltd.