In this research parallel molecular dynamics (MD) simulations have been performed to study the deformation behavior of nanocrystalline copper samples with embedded nanotwins under approximately uniaxial tensile load. Simulation results reveal that twin boundaries (TBs) act as obstacles to dislocation movements that lead to the strengthening of nanotwinned structures. However, easy glide of dislocations parallel to the TBs contribute primarily to the plastic strain or ductility of these materials. At higher deformation stages, the strengthening effects reach a maximum when abundant dislocations begin crossing the TBs. Due to this highly anisotropic plastic response of the grains, a random polycrystalline sample will show combined properties of ductility and strength. The strengths of the nanotwinned models are found to exhibit an inverse relationship with the twin width and temperature. We also investigate the relation between the deformation behavior in different grains, their orientation with respect to the loading direction, and ultimately the observed response of nanotwinned structures.