In the present work, study of the vibration of a functionally graded (FG) cylindrical shell made up of stainless steel, zirconia, and nickel is presented. Free vibration analysis is presented for FG cylindrical shells with simplysupported-simply supported and clamped–clamped boundary condition based on temperature independent material properties. The equations of motion are derived by Hamilton’s principle. Material properties assume to begraded in the thickness direction according to a simple power law distribution in terms of the volume fraction of the constituents. Effects of boundary conditions and volume fractions (power law exponent) on the naturalfrequencies of the FG cylindrical shell are studied. Frequency characteristics of the FG shell are found to be similar to those of isotropic cylindrical shells. Furthermore, natural frequencies of these shells are observed to be dependent on the constituent volume fractions and boundary conditions. Strain displacement relations from Love s and first-order shear deformation theoriesare employed. Galerkin method is used to derive the governing equations for clamped boundary conditions. Further, analytical results are validated with those reported in the literature and excellent agreement is observed. Finally,in order to investigate the effects of the temperature gradient, functionally graded materials cylindrical shell with high temperature specified on the inner surface and outer surface at ambient temperature,1D heat conduction equation along the thickness of the shell is applied and the results are reported.