Recent observations, such as the magnetic field strength decrease, a magnetic poles shifts and the South Atlantic anomaly increase, may indicate the beginning of the Earth’s magnetic field inversion. According to the geomagnetic dynamo model, the dipole component of the magnetic field is zeroed at the inversion time, and the quadrupole one becomes dominant. To assess the occurrence of radiation hazards on the Earth’s surface and in near-Earth space at the time of magnetic field inversion, a numerical model was developed that made it possible to compare the GCR and SCR fluxes (at minima and maxima of solar activity) penetrating the Earth (taking into account the atmosphere) and the ISS in periods of the dipole and quadrupole fields dominance. It was found that during the period of inversion the flow of GCR (high-energy particles) can increase no more than three times over the entire surface of the Earth and the radiation dose will not exceed permissible one for man. Also, a change of the magnetic field configuration will redistribute areas of increased radiation on the Earth’s surface (today these are the poles of the Earth), which can adversely affect people’s health in these areas.