The construction of metallic nanocrystalline (NC) samples by molecular dynamics simulation is investigated. Firstly, the initial NC aluminum and copper samples are assembled by Voronoi geometrical construction method, then the local minimized energy states of the samples are obtained by quenching (or conjugate gradient method). Finally, the simulated annealing method in normal pressure and temperature condition ensembles at zero pressure is used to approximate the global minimized energy states of the samples. The residual internal stress is employed to signify the difference between the simulated and the experimentally synthesized samples for the first time. The structure of grain boundaries, the descending process and the local distribution of the average internal stress and the energy of the samples, as well as the elastic constants of the final samples are observed during these two relaxation procedures. It is found that the energy and the residual internal stress of the samples are close to the experimental data after relaxation. It is enough to obtain the global minimum energy states through Voronoi geometrical construction to investigate the static and dynamic mechanical properties of NC metals with a 5—10 ps local energy minimization and a 40—100 ps of simulated annealing with annealing temperature between the room temperature and 65% of melting point. The annealing time and temperature are of little importantce to the mechanical properties within the parameter windows properly selected.