The process of storing and redistributing hydrogen atoms under the action of pulse high-temperature hydrogen plasma obtained on the PF-4 plasma focus (PF) plant in an assembly of three high-purity niobium foils is studied by the elastic recoil detection (ERD) method. It is determined that, as the number of hydrogen plasma pulses increases, the implanted hydrogen atoms are redistributed at larger depths in an assembly of niobium foils which significantly exceed the projected range of hydrogen ions (when their maximal velocity reaches ∼108 cm/s). A maximum hydrogen concentration of up to 60 at % is reached in the nearest (to PF-4) surface of the third Nb foil under the action of 20 hydrogen plasma pulses. The observed phenomenon can be attributed to the ejections of implanted hydrogen atoms under the action of high-power shock waves created in niobium foils by the pulse hydrogen plasma and/or by the accelerating diffusion of hydrogen atoms under the action of compression-straining waves at the front of the shock wave with redistributions of hydrogen atoms at larger depths. Similar behavior is found in assemblies of two or three and more nickel, vanadium, niobium, and tantalum foils of different thicknesses, including foil assemblies made of heterogeneous materials, which were also studied.