The invention relates to a so-called stabilization method, consisting of completing the filling of traveling egg trays. In each of the successive trays, eggs taken from an available egg reservoir are deposited in empty locations. This reservoir is made up of egg receiving cells that are movable along rows of cells in series. Depending on a filling state of the tray being treated identifying the distribution of the empty locations relative to the full locations, the reservoir is automatically configured in a configuration of egg-bearing cells complementary to said filling state of the tray in progress, so as to next transfer eggs between the reservoir and the tray in progress by correspondence between empty locations and full locations in the tray and the presence or absence of an egg-bearing cell in the reservoir.