This paper presents a simulation study on the compaction of mono-sized spherical particles systems under symmetric vibration. The in uence of the vibration amplitude on the density after 500 000 vibration cycles and on the dynamics of vibration is ÿrst studied. It is shown that vibration brings the initial packing to a "suspension" where the distance between particles depends on the vibration amplitude. A large vibration amplitude (D=10) leads to a crystallization of the system whereas a small vibration amplitude induces an e cient compaction of the packing. The vibration procedure is then modiÿed by decreasing the vibration amplitude during compaction in order to speed up the densiÿcation of the system and to reach high packing densities. Packing densities ranging from 0.64 up to 0.69 are easily obtained. In the latter case (obtained with an initial vibration amplitude of D=10), a crystallization of the packing is initiated along the at walls of the container and progresses towards the bulk packing. Finally, the in uence of the boundary conditions is studied. It is shown that a random granular boundary condition also leads to a crystallization of the system for a large initial vibration amplitude (D=10). The order that appears amongst the system is due, in that case, to the vibration procedure itself and not to the boundary conditions.