Abstract <p>The gas bremsstrahlung field generated by an electron beam of a synchrotron during interactions with particles of the residual gas in the vacuum chamber has been calculated. The calculations have been performed for the vacuum chamber of the storage ring of the synchrotron with an electron energy of 6 GeV, which corresponds to the beam energy of the ESRF synchrotron (France) and the SILA synchrotron project (Russia). The radiation situation near the direction of gas bremsstrahlung propagation is considered. Secondary charged particles and photoneutrons produced by electromagnetic cascades in combination with photonuclear reactions are taken into account. The radiation fields generated during synchrotron operation are simulated by the Monte Carlo method using the GEANT4 software package. The angular and spectral distributions of gas bremsstrahlung near the vacuum chamber are presented, as well as the results for the effective dose rate near the axis of the synchrotron radiation extraction line.</p>