This book was an attempt to study the wave dispersion characteristics of a carbon nanorod through Second, Fourth, Sixth and Eighth orders nonlocal strain gradient models. Expressions are derived for both wave number and wave speeds of the nanorod. The wave characteristics of the nanorod obtained from the nonlocal strain gradient models are compared with the classical continuum model. From these models it is observed that sixth order strain gradient model gives the better approximations than the second and fourth order strain gradient models for dynamic analysis. The second and sixth order strain gradient models gives a critical wave number at a certain wave frequency which does not exist in fourth and eight order strain gradient models. Eringen’s nonlocal theory of elasticity is applied to study the wave properties of single walled carbon nanotubes. The effects of wave number and nonlocal scaling parameter (e0a) on the frequency ,phase velocity and group velocity are discussed for a particular material of carbon nanotube.