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This paper presents a study of the gamma-ray induced radiation damage effect in large size (2.5 times 2.5 times 20 cm3) LSO and LYSO crystal samples. Optical and scintillation properties, including longitudinal transmittance and photo-luminescence spectra, light output and light response uniformity with PMT and APD readout, are measured before and after gamma-ray irradiations with an integrated dose up to 106 rad for three LSO and LYSO samples from different vendors. It was found that 300degC thermal annealing removes all radiation induced absorption. The photo-luminescence spectra measured before and after the irradiations were found to be consistent, indicating that the scintillation mechanism is not damaged. The radiation damage recovers very slow under the room temperature, indicating that the radiation damage level in LSO and LYSO crystals is not dose rate dependent. It was also found that the overall radiation damage in LSO and LYSO crystals is small as compared to other crystal scintillators commonly used in high energy and nuclear physics experiments.