This paper aims at the elastic buckling of multilayered thin-walled conical shells with power-law distributed material properties under the axial load and lateral pressure based on the experimental study of palm trunks. The material properties of the shells are assumed to vary continuously in the radial direction. Relations and analytical approaches for linear buckling response are presented by using the layer-wise shell theory. The buckling behaviors of the conical shells subjected to axial and transverse loads are investigated. Parametric study in geometry(relative thickness, relative stiffness and cone angle) is performed to enhance the overall buckling resistance and minimize the weight. Numerical results show the possibility to achieve larger load-carrying capacity by simultaneously optimizing the material and geometric parameters based on the structure of palm trunks.