Carbon nanomaterials such as vertically aligned carbon nanotubes arrays are emerging new materials that have demonstrated superior mechanical, thermal, and electrical properties. The carbon nanomaterials have the huge potential for a wide range of vehicular applications, including lightweight and multifunctional composites, high-efficiency batteries and ultracapacitors, durable thermal coatings, etc. In order to design the carbon nanomaterials for various applications, it is very important to develop effective computational methods to model such materials and structures. The present work presents a structural mechanics approach to effectively model the mechanical behavior of vertically aligned carbon nanotube arrays. The carbon nanotube may be viewed as a geometrical space frame structure with primary bonds between any two neighboring atoms and thus can be modeled using three-dimensional beam elements. Effects of tube geometric factors (wall thickness and tube diameter) and material properties (Poisson's ratio) on mechanical properties of the nanotube structure were examined. Results show that the Young's modulus is inversely proportional to the nanotube wall thickness and Poisson's ratio. On the other hand, the Young's modulus and shear modulus exhibit nonlinear relationships with the nanotube diameter, i.e., both moduli increase rapidly at smaller diameters but become stabilized at larger diameters. Compression test conducted on VACNT array shows linear behavior for the values of applied strains in the present case.