Carbon nanotubes have been the main focus in science and engineering fields lately for their extraordinary properties. But carbon nanotube fabrication process is very expensive, particularly for reinforcements and structural composite applications. Instead of working towards developing lower cost nanotubes, an alternate solution to resolve the problem is to formulate a cost effective reinforcement referred to as graphene nanoplatelets. These nanoplatelets have excellent mechanical as well as electronic properties opening up for several applications in various fields. Their structure with carboncarbon bonds make them stronger and stiffer. Single nanotubes can be used as reinforcements in one direction, while the graphite nanoplatelets are effective in two directions yielding a higher degree of stiffness and strength in a matrix In this thesis, a molecular dynamic computer simulation technique was used to explore the atomic scale and dynamics of graphene nanoplatelets and carbon nanotubes embedded in polyethylene matrix. The mechanical properties of the carbon nanotubes and nanoplatelets polymer composite models were studied individually along with a comparison between composite models. The overall system was modeled using material studio software with the implementation of periodic boundary conditions to determine the properties. The stress strain curves revealed that the length and the volume fraction of the nanotube/nanoplatelets had a significant effect on the mechanical properties of the composite. The stiffness of the composite with long reinforcement length increased relative to the polymer in the longitudinal direction and shows an anisotropic behavior. Significant enhancement was observed in the Young's modulus with the increase in the volume fraction of the nanotubes/nanoplatelets because of the well known effect of the increase in the load transfer between the polymer and the reinforcements. Also increasing the volume fraction of the short nanotubes/nanoplatelets provided very little improvement in stiffness compared to the longer length nanotubes/nanoplatelets. Results also showed that the graphene nanoplatelet reinforced composite properties were very comparable to the nanotubes reinforced composites even under weak vander Waal interactions.