Recently, carbon nanotubes are considered as nanoscale fibers, which can strengthen polymer composite materials. Nanotube-polymer composite materials can be used for micron scale devices with designed mechanical properties and smart polymer coating to protect materials under extreme physical conditions such as microsatellites. To explore these possibilities it is important to develop a detailed atomic scale understanding of the mechanical coupling between polymer matrix and embedded nanotubes. In this work we study the chemical bonding between polymer molecules and carbon nanotubes (CNTs) using molecular dynamics. Study shows that the bonding between polyethylene and a CNT is energetically favorable. Chemical bonds can be formed at multiple sites, which make the mechanical load transfer from the polymer chain to the tube more favorable. We will discuss about the resulting mechanical coupling between the CNTs and polymer matrix to develop efficient nano-composite materials.