Using molecular dynamic (MD) simulation, the mechanical properties of a buckypaper/epoxy composite were calculated. In order to simulate a large model within a large enough timescale, a general MD code fully implemented on graphical processing units (GPUs) was developed. The code, which enables the simulation of large systems with about five hundreds speed up in simulation time relative to a single CPU core, is capable of running on CUDA enabled GPUs. In this study the buckypaper/epoxy composite consists of single wall carbon nanotubes (CNTs), epoxy resin (EPON-862) and the curing agent diethyltoluenediamine (DETDA). Next, the mechanical properties of buckypaper/epoxy composite, namely elastic modulus and Poisson's ratio, were studied through the simulation of a set of tension tests. For the first time directional properties of this material is calculated. A comparison with previously published data is also included. The results prove that the proposed procedure is suitable for investigating the mechanical properties of the buckypaper/epoxy composites. In addition, the results show a negative Poisson ratio and high modulus of elasticity for the buckypaper/epoxy composites, which proves the application of such material in producing artificial muscles, and advanced composites in aviation industries, respectively. Finally, a study on the failure mechanisms of the material is conducted and the integrity of the results was checked by the available experimental and analytical data.