This article presents an investigation on the buckling of functionally graded (FG) truncated conical shells under an axial load resting on elastic foundations within the shear deformation theory (SDT). The governing equations are solved using the Galerkin method, and the closed-form solution of the axial buckling load for FG conical shells on elastic foundations within the SDT is obtained. Various numerical examples are presented and discussed to verify the accuracy of the closed-form solution in predicting dimensionless buckling loads for FG conical shells on the Winkler-Pasternak elastic foundations within the SDT.