  We have modelled the hard X-ray background expected for a high-altitude
balloon flight of the Energetic X-ray Telescope Experiment (EXITE2), an imaging
phoswich detector/telescope for the 20--600 keV energy range. Photon and
neutron-induced contributions to the background are considered. We describe the
code and the results of a series of simulations with different shielding
configurations. The simulated hard X-ray background for the actual flight
configuration agrees reasonably well (within a factor of $\sim$ 2) with the
results measured on the first flight of EXITE2 from Palestine, Texas. The
measured background flux at 100 keV is $\sim$ 4 $\times$ 10$^{-4}$ counts
cm$^{-2}$ s$^{-1}$ keV$^{-1}$.
