Studying of connection between a carbon nanotube (CNT) and its surrounding matrix is an important issue in investigation of the behavior of nanocomposites reinforced with carbon nanotubes. In this paper, the carbon nanotube and its surrounding matrix is considered as a volume element and its mechanical behavior is analyzed using finite element method. Interface joints are modeled utilizing nonlinear spring elements; and effective force between CNT and matrix is determined based on Lennard-Jones equation. The interface thickness is changed between 1.7-3.8Am, to study its effect on the volume element behavior. Tensile loading of volume element is applied in two ways to investigate the perfect connection between nanotube and matrix. Subsequently, tensile longitudinal elastic modulus of volume elements with different aspect ratios of nanotube and thickness of interface are calculated and compared with the results of rule of mixture theory in micro mechanics field. The results of this research indicate that for low aspect ratios, the amount of elastic modulus is near to individual resin or nanotube. But, increasing the aspect ratio causes the connections to be more efficient and results converge to rule of mixture