Many experimental and theoretical studies have been performed on single and multi-wall nanotubes. In particular, deformation modes and overall tube stiffness have been examined. This problem will be even more challenging in the case of nanocomposites in which carbon nanotubes are dispersed randomly in a polymeric (i.e. polystyrene, epoxy etc.) matrix. A critical issue for nanotechnology is the ability to understand, model and simulate the behavior of the small structures and to make the connection between structure properties and functions. Most nanosystems are too small for direct measurements but too large to be described by current rigorous first principles in theoretical and computational methods. They exhibit too many statistical ensembles. The vital role of molecular modeling in this field is to enable engineering design at the component and systems level and to set objectives that could guide laboratory efforts of the physical implications. An important component in molecular mechanics calculations of the nanostructure of materials is the description of the forces between individual atoms which are characterized by a force field. In this paper, the stiffness matrix of a single wall carbon nanotube (SWCNT) of (7, 0) chirality is calculated using molecular dynamics simulation under various combinations of loads. Both the magnitude and direction of load are varied on SWCNT and its composites. When dispersed in the polymeric matrix, it was observed that SWCNTs tend to cluster in bundles. Bundles of 7, 9 and 19 SWCNT (7, 0) are modeled using molecular dynamics and the stiffness matrix is calculated for all the three cases. The polymeric matrix is simulated and its mechanical properties are calculated. SWCNT-polymer nanocomposite is then modeled using a single wall carbon nanotube embedded in a polymeric matrix. Also, the mechanical properties of the interface for the same nanocomposite are calculated. In this case, the density of the SWCNT-polymer nanocomposite in the vicinity of SWCNT is maintained to match the experimentally observed density of the same kind of nanocomposite.