  Measuring external sources of background for a deep underground laboratory at
the Homestake Mine is an important step for the planned low-background
experiments. The naturally occurring $\gamma$-ray fluxes at different levels in
the Homestake Mine are studied using NaI detectors and Monte Carlo simulations.
A simple algorithm is developed to convert the measured $\gamma$-ray rates into
$\gamma$-ray fluxes. A good agreement between the measured and simulated
$\gamma$-ray fluxes is achieved with the knowledge of the chemical composition
and radioactivity levels in the rock. The neutron fluxes and $\gamma$-ray
fluxes are predicted by Monte Carlo simulations for different levels including
inaccessible levels that are under construction for the planned low background
experiments.
