in this study, a formulation for the stability of cylindrical thin shells made of functionally graded material (FGM) subjected to torsional loading varying as a linear function of time is presented. The properties are graded in the thickness direction according to a volume fraction power law distribution. The modified Donnell type dynamic stability and compatibility equations are obtained. Applying Galerkin's method then applying Lagrange-Hamilton type principle to these equations taking the large values of loading speed into consideration, analytic solutions are obtained for critical torsional parameters values. The results show that the critical torsional parameters are affected by the configurations of the constituent materials variations. Comparing results with those in the literature validates the present analysis. (C) 2004 Elsevier Ltd. All rights reserved.