A free vibration analysis of metal and ceramic functionally graded conical shell panels is presented using the element-free kp-Ritz method. The first-order shear deformation shell theory is used to account for the transverse shear strains and rotary inertia, and mesh-free kernel particle functions are employed to approximate the two-dimensional displacement fields. The material properties of the conical shell panels are assumed to vary continuously through their thickness in accordance with a power-law distribution of the volume fractions of their constituents. Convergence studies are performed in terms of the number of nodes, and comparisons of the current solutions and those reported in literature are provided to verify the accuracy of the proposed method. Two types of functionally graded conical shell panels, including Al/ZrO2 and Ti–6Al–4V/aluminum oxide, are chosen in the study, and the effects of the volume fraction, boundary condition, semi-vertex angle, and length-to-thickness ratio on their frequency characteristics are discussed in detail.