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A combined passive shield of the RED-100 two-phase emission neutrino detector has been developed and built for suppressing the background of external γ rays and neutrons. The shield is composed of a 5-cm-thick copper layer (the inner layer is adjacent to the detector) and a water layer with a total thickness of approximately 70 cm (including the water inside the copper shield). The Monte Carlo simulation of the shielding efficiency has been performed. The obtained attenuation factor of the copper shield for the γ-ray background has been experimentally verified in a laboratory test using a NaI(Tl) scintillator detector. The γ-ray background rejection factor of the full shield has also been calculated.