We present a numerical method capable of reproducing the densification process from the so-called random loose to dense packing of uniform spheres under vertical vibration. The effects of vibration amplitude and frequency are quantified, and the random close packing is shown to be achieved only if both parameters are properly controlled. Two densification mechanisms are identified: pushing filling by which the contact between spheres is maintained and jumping filling by which the contact between particles is periodically broken. In general, pushing filling occurs when the vibration intensity is low and jumping filling becomes dominant when the vibration intensity is high.