Linear and mass ranges of protons and argon ions in aluminum, alumina, bismuth, and W77.7Cu22.3 composite shields were calculated using the SRIM software package. It is shown that the protection efficiency against high-energy ions by materials with large atomic charge (Z) values is higher, from the position of linear ranges of particles, and lower, from the position of mass ranges, in comparison with materials with low Z values. The dependence of the threshold energy on the serial number of particles for aluminum, bismuth, and composite W77.7Cu22.3 shields is determined. The ionization loss spectra for the passage of both protons with an energy of 20 MeV and krypton ions with an energy of 7.75 GeV through multilayer Bi/Al/Al2O3 and Al/Al2O3/Bi structures were calculated. These results showed that the braking of high-energy particles in the case when the first layer contains a heavy element is higher than in the case when the first layer contains a light element. The influence of the sequence in the arrangement and thickness of the layers in the multilayer structures of the Bi/Al/Al2O3 system on the efficiency of protection against high-energy ions was studied. It is shown that the nature of the dependences R(E) and ion energy losses are determined by the sequence of arrangement of individual layers, which is due to the difference in the conversion of the spectra by the material of the first layer. The studied radiation shields can be used in aerospace and nuclear technologies, as well as in many scientific and medical devices, and can be used to protect against the effects of a wide range of ionizing radiation (electrons, protons, heavy charged particles, etc.).