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The aim of this study was to determine the attenuation of gamma and X-rays with different energies caused by passage through different materials. To this end, different materials with a range of atomic numbers were chosen to measure gamma and X-ray attenuation coeffi-cients and to explore the mechanisms of interaction of gamma and X-rays with matter of various kinds. It is shown that the attenuation coefficients first decrease and then increase with increase in the radiation (photon) energy. The attenuation of gamma and X-rays passing through materials with high atomic number is greater than that in materials with low atomic number. The attenuation minimum is related to the atomic number of the irradiated materials. The larger the atomic number is, the lower the energy corresponding to attenuation minimum is. Photo-electric and Compton effects are the main processes when gamma rays pass through individual materials with high and low atomic numbers, respectively. Therefore, for radiotherapy and radiation protection, different methods should be considered and selected for the use of gamma and X-rays of different energies for use in different materials.