In most barrier applications, both mechanical and diffusion properties of the material are important. In this thesis the evaluation of molecular mechanisms responsible for the enhanced elastic properties of Polymer Clay Nanocomposites (PCNs) and the molecular mechanisms of Oxygen diffusion in PolyButylene Terephthalate polymer are presented. Interaction energy between PCN constituents, conformational changes of polymer, interaction energy between Oxygen molecule and polymer, rate of Oxygen and Oxygen diffusion coefficient are evaluated. Molecular simulation studies of PolyButylene Terephthalate (PBT) clay nanocomposite and Nylon6 clay nanocomposite show that a higher crystallinity polymer such as PBT would require higher attractive and repulsive interactions with organic modifier in order to make significant change in the crystallinity of PBT in the nanocomposite and in turn enhance the elastic modulus and hardness. Molecular interactions energy between Oxygen molecule and polymer, change in polymer conformation caused by thermal energy assist the Oxygen molecule to diffuse through polymer.