The natural frequencies (f) as a function of the length (L) of single multi-walled carbon nanotubes (CNTs) are measured using the electric-field-induced resonance method together with the "nanoknife" technique for cutting nanotubes to the desired length. The experimental f-L data for short CNTs are found to be adequately described by the Timoshenko beam model, but not by the widely-used Euler-Bernouilli beam model. The failure of the Euler-Bernouilli beam model is due to its neglect of the significant effect of shear deformation caused by the extremely-anisotropic mechanical properties of CNTs. The axial Young's modulus and radial shear modulus of CNTs are obtained simultaneously through fitting the experimental f-L data with the Timoshenko beam model.