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The ground level enhancements (GLEs) due to solar cosmic rays (SCRs) are of significant interest for a number of astrophysical and geophysical tasks related to a planetary processes on the Earth. In the present work the ionization rate profiles in the Earth’s atmosphere during the GLE65 on 23 February 1956 and GLE67 are obtained. The ionization in the atmosphere is calculated with RUSCOSMICS (c) software package (based on GEANT4 of CERN) using the energetic spectra of solar protons and corresponding atmospheric cascade simulation. The spectra of solar cosmic rays are obtained with the Neutron Monitor ground-based measurements and methods developed at the Polar Geophysical Institute (Apatity) of the Russian Academy of Sciences. This method is based on solving of the inverse problem – a SCR spectrum reconstruction on the boundary of the magnetosphere. The energy deposit of solar protons in the atmosphere is calculated and the ion production rate profiles in the stratosphere and troposphere (the region 0–40 km) are presented for geomagnetic cut-off rigidities 1, 2, 3 and 5 GV (i.e. higher-polar and middle latitudes). Also the secondary particles energy spectra characterizing the development of a cascade in the Earth's atmosphere are shown. The model experiment data are compared with the data derived on the balloon flights and are in good agreement with them.