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CUORE is a 1 ton scale cryogenic experiment aiming at the measurement of the Majorana mass of the electron neutrino. The detector is an array of 988 TeO
2 bolometers used for a calorimetric detection of the two electrons emitted in the
β
β
(
0
ν
)
of
130Te. The sensitivity of the experiment to the lowest Majorana mass is determined by the rate of background events that can mimic a
β
β
(
0
ν
)
. In this paper, we investigate the contribution of external sources i.e. environmental gammas, neutrons and cosmic ray muons to the CUORE background and show that the shielding setup designed for CUORE guarantees a reduction of this external background down to a level <10
−2
counts/kg
keV
yr at the
Q-value, as required by the physical goal of the experiment.