Abstract: Free vibration of carbon nanotubes is analyzed by the meshless method. Several numerical examples are used to verify the convergence of the present method. The natural frequencies of the carbon nanotubes of different length-to-diameter ratios are calculated and compared with the available results in published literature. The results show that the present method enjoys a high accuracy, and the meshless method based on the thin-plate spline radial basis function can successfully be used to analyze the free vibration of carbon nanotubes.