AbstractThis paper presents a mechanical and thermal buckling analysis of metal and ceramic functionally graded conical shell panels using the element‐free kp‐Ritz method. The formulation is based on the first‐order shear deformation shell theory, which accounts for the transverse shear strains and rotary inertia, and mesh‐free kernel particle functions are employed to approximate the two‐dimensional displacement fields. The effective material properties of the functionally graded conical shell panels are assumed to be smooth and continuous through their thickness direction, and are determined according to a power‐law distribution of the volume fractions of their constituents. Convergence studies are performed in terms of the number of nodes, and comparisons between the current solutions and those reported in the literature are provided to verify the accuracy of the proposed method. Three types of functionally graded conical shell panels, Al/ZrO2, SUS304/Si3N4, and Al2O3/Ti−6Al−4V are selected for study, and the effects of the volume fraction, boundary condition, semi‐vertex angle, length‐to‐thickness ratio, and temperature‐dependent material properties on the buckling strength are discussed in detail. Copyright © 2010 John Wiley & Sons, Ltd.