Here a method for data storage by means of multiplexing 3D holograms is considered. The method consists in shifting the recording material with respect to a reference speckle wave. The experimental data on the dependence of the diffraction efficiency of the hologram with respect to the shift is presented. The general scheme of data storage in 3D-speckle shift hologram is considered and presented. It's shown that this kind of hologram substantially outperforms all other types for the number of cells (pixels) in which information can be stored. At the same time, the noises that are inherent in a 3D-speckle shift hologram restrict the density of the information storage.