The potential of filling carbon nanotubes in polymers has been widely acknowledged for composites with exceptional new properties owing to the high strength of carbon nanotubes. In the thesis, by employing Materials Studio 4.0 software, the buckling behaviour and vibration of polyethylene and carbon nanotube matrix composites are first discussed using molecular mechanics simulations. The research is aimed to acquire a high strength design of PE-CNT matrix with proper PE/CNT ratio as well as discovering the dynamic characteristics of the PE-CNT composites. Investigation results show that as the number of PE chains increases, the buckling strain and the resonance frequency will decrease. Van der Waals forces are collected to explain the relation of the PE chains to the buckling strain and the resonance frequency of the composites.