Abstarct: In this work, an attempt was made to study the mechanical properties of polyethylene composites reinforced with single walled-carbon nanotubes. The aim of this study was to investigate the effect of volume fraction and aspect ratio of CNT on mechanical properties of composite. Molecular dynamics simulation was used for this purpose. First, a relaxed structure from Polyethylene and another relaxed structure of nanocomposite was obtained. Then a strain of about 0.5% was applied to the simulation cell to obtain longitudinal and transverse elastic modulus and longitudinal shear modulus. The results of the molecular dynamics simulation showed that the elastic properties of the composite improved along the orientation of the fibers. Young's modulus and shear modulus of composites increased after adding more nanotubes. Finally, the values obtained from the molecular dynamics simulation, related to the Young's modulus and the shear modulus of the composite, were compared with the values obtained from the Rule of Mixture, periodic microstructure model, the Halphin-Tsai and Mori-Tanaka, indicating a slight divergence between the results of the molecular dynamics and the mathematical models.