Elastic and engineering properties of nanoparticle enhanced composites and their constituents (matrix, reinforcement and interface) are calculated. The nanocomposites considered in this study consist of a single-wall carbon nanotube (SWCNT) embedded in polyethylene matrix. Molecular dynamics simulations are used to estimate the elastic properties of SWCNT, interfacial bonding, polyethylene matrix and composites with aligned and randomly distributed SWCNTs. The elastic properties of bundles with 7, 9, and 19 SWCNTs are also compared using a similar approach. In all simulations, the average density of SWCNT-polymer nanocomposite was maintained in the vicinity of CNTs, to match the experimentally observed density of a similar nanocomposite. Results are found to be in good agreement with experimentally obtained values by other researchers. The interface is an important constituent of CNT-polymer composites, which has been modeled in the present research with reasonable success.