Resonant frequencies and the associated vibrational modes of multiwall carbon nanotubes are studied in this paper. The analysis is based on a multiple-elastic beam model, considering intertube radial displacements and the related internal degrees of freedom. Especially, van der Waals interaction is modified considering both all interaction between each layers in multi-wall carbon nanotubes and curvature effect. The results show that modified van der Waals interaction could significantly affect the natural frequencies of multi-walled carbon nanotubes. In particular, non-coaxial intertube resonance will be excited at the higher resonant frequencies of multiwall carbon nanotubes.