A new methodology for determining the radial elastic modulus of a one-dimensionalnanostructure laid on a substrate has been developed. The methodology consists of thecombination of contact resonance atomic force microscopy (AFM) with finite elementanalysis, and we illustrate it for the case of faceted AlN nanotubes with triangularcross-sections. By making precision measurements of the resonance frequencies of the AFMcantilever-probe first in air and then in contact with the AlN nanotubes, we determine thecontact stiffness at different locations on the nanotubes, i.e. on edges, inner surfaces,and outer facets. From the contact stiffness we have extracted the indentationmodulus and found that this modulus depends strongly on the apex angle of thenanotube, varying from 250 to 400 GPa for indentation on the edges of the nanotubesinvestigated.