The non-local formulation of elasticity has been introduced as a correction to the local theory in order to account for long ranged inter-atomic forces. This elasticity theory is useful to estimate the in-plane stiffness of Single Wall Carbon Nanotube. The non- local effect is present in Single Wall Carbon Nanotube through the introduction of a non-local nanoscale which depends of the material and a molecular internal characteristics length. This non-local nanoscale goes to zero at macro scale and hence the non-local effect vanishes with reference to classical mechanics. The resulting from the non-local elasticity theory is verified through molecular simulations results. For this study of non-local theory in analysis of Carbon Nanotube, the value of scale coefficient is about 0.7nm.