An analytical formulation is presented for vibration and buckling analyses of clamped conical shells made of functionally graded materials (FGMs) under various uniform pressures. It is assumed that the shell is a metal and ceramic mixture and its properties change as a function of the shell thickness. In this study, both types of FGM, power and exponential, are taken into account together. The governing equations according to the Donnell's theory are solved by Galerkin's method and the critical hydrostatic and lateral pressures and fundamental frequencies have been found analytically. To solve this problem, an unknown parameter lambda is included in the approximation functions. Furthermore, parameter lambda, which is included in the obtained formulas, is taken from the minimum conditions of critical stresses and frequencies. The different generalized values are obtained for the parameter lambda for buckling pressures and frequencies of cylindrical shells, and truncated and complete conical shells with clamped edges. Several examples are presented to show the accuracy and efficiency of the formulation. The closed-form solutions are verified by accurate different solutions. Effects of changing radius-to-thickness ratio, lengths-to-radius ratio, material composition, and volume fraction of constituent materials on the critical parameters of truncated and complete conical shells are also investigated.