Key improvements in the sensitivity of the underground particle astrophysics experiments can only be achieved if the radiation causing background events in detectors is well understood and proper measures are taken to suppress it. The background radiation arising from radioactivity and cosmic‐ray muons is discussed here together with the methods of its suppression. Different shielding designs are considered to attenuate gamma‐rays and neutrons coming from radioactivity in rock and lab walls. Purity of materials used in detector construction is analysed and the background event rates due to the presence of radioactive isotopes in detector components are discussed. Event rates in detectors caused by muon‐induced neutrons with and without active veto systems are presented leading to the requirements for the depth of an underground laboratory and the efficiency of the veto system.