In this study, an analytic solution is provided for the stability and vibration behavior of truncated conical shells composed of Si3N4 and SUS304 under the axial compressive load. The material properties of the FG conical shells are assumed to vary continuously through the thickness of the shell according to quadratic and inverse quadratic distribution of the volume fraction of the constituents. The fundamental relations and governing equations for thin conical shells composed of Si3N4 and SUS304 is obtained by using Love's shell theory and a solution is obtained by applying Galerkin's method. The effects of the constituent volume fractions on the critical axial load and frequency parameter of the truncated conical shell are also elucidated.