  The Cryogenic Underground Observatory for Rare Events (CUORE) is designed to
search for neutrinoless double beta decay of 130Te with an array of 988 TeO2
bolometers operating at temperatures around 10 mK. The experiment is currently
being commissioned in Hall A of Laboratori Nazionali del Gran Sasso, Italy. The
goal of CUORE is to reach a 90\% C.L. exclusion sensitivity on the \tect decay
half-life of 9$\times$10$^{25}$ years after 5\,years of data taking. The main
issue to be addressed to accomplish this aim is the rate of background events
in the region of interest, which must not be higher than
10$^{-2}$\,counts/keV/kg/y. We developed a detailed Monte Carlo simulation,
based on results from a campaign of material screening, radioassays, and
bolometric measurements, to evaluate the expected background. This was used
over the years to guide the construction strategies of the experiment and we
use it here to project a background model for CUORE. In this paper we report
the results of our study and our expectations for the background rate in the
energy region where the peak signature of neutrinoless double beta decay of
130Te is expected.
