In this paper, a formulation for the buckling of cylindrical thin shells made of functionally graded material (FGM) composed of ceramic and metal subjected to external pressure varying as a power 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 using Love's shell theory. Applying Galerkin's method and then applying a Ritz type variational method to these equations for different initial conditions and taking large values of the loading parameters into consideration, analytic solutions are obtained for critical parameter values. The results show that the critical parameters are affected by the configurations of the constituent materials, loading parameters variations and the power of time in the external pressure expression variations. Comparing the results with those in the literature validates the present analysis.