The GEANT 4.9.2 software package is applied for the simulation of primary and Compton scat tered bremsstrahlung spectra. The possibility of restoring primary γ radiation spectra with the energy 0.02-1200 MeV using Compton scattering on secondary scattering targets is studied. The advantages of light targets using are demonstrated. An additional bremsstrahlung contribution from e ± pairs is calculated for high energy γ quanta; the influence of CXR on the form of scattered X ray quantum spectra is estimated. The spec tra which have a multipeak structure are restored. For high energy γ quanta there occurs significant spread of energies in the Compton scattered radiation spectrum, which imposes stringent conditions on collimation and detector resolution capability. The possibility of measuring the bremsstrahlung spectra from a primary target during high angle Compton scattering is estimated.