  The XENON100 experiment, installed underground at the Laboratori Nazionali
del Gran Sasso (LNGS), aims to directly detect dark matter in the form of
Weakly Interacting Massive Particles (WIMPs) via their elastic scattering off
xenon nuclei. This paper presents a study on the nuclear recoil background of
the experiment, taking into account neutron backgrounds from ($\alpha$,n) and
spontaneous fission reactions due to natural radioactivity in the detector and
shield materials, as well as muon-induced neutrons. Based on Monte Carlo
simulations and using measured radioactive contaminations of all detector
components, we predict the nuclear recoil backgrounds for the WIMP search
results published by the XENON100 experiment in 2011 and 2012,
0.11$^{+0.08}_{-0.04}$ events and 0.17$^{+0.12}_{-0.07}$ events, respectively,
and conclude that they do not limit the sensitivity of the experiment.
