Results are presented on the effects of radiation on BGO crystals. It is shown that BGO has more than two orders of magnitude higher resistance against low energy γ rays than SF5 lead glass. Darkening of the crystal is hardly visible even after an irradiation of 3.6 × 10 6 R. The darkening faded by more than one half after several days and it has almost completely disappeared after much longer periods. The tolerable rate of synchrotron radiation on BGO calorimeters is 100 R/h in a conservative estimate if the degradation in transmittance is required to be less than 1 % over a depth of 20 radiation lengths. In BGO calorimeters, the degradation of scintillation efficiency is less important than that of the transmittance, 99.999% pure crystals have a two orders of magnitude better resistance than 99.99% pure ones. Sample darkening caused by 12 GeV protons or fast neutrons is an order of magnitude more severe than that by low energy γ rays. Moreover, the recovery is not complete even after a period of more than 100 days. Some data on sample activation are also presented.