  Annual modulation of $\gamma$ rays from ($\alpha$, $\gamma$) reactions in the
Soudan Underground Lab has been observed using a 12-liter scintillation
detector. This significant annual modulation, measured over 4 years, can mimic
the signature for dark matter and can also generate potential background events
for neutrinoless double-$\beta$ decay experiments. The measured annual
modulation of the event rate from ($\alpha$, $\gamma$) reactions is strongly
correlated with the time-varying radon concentration observed independently in
the Lab. The $\alpha$ flux from radon decay is simulated starting from the
measured radon concentration, and the $\gamma$-ray flux is determined using the
convolution of the $\alpha$ flux and the cross sections for ($\alpha$,
$\gamma$) reactions. The calculated $\gamma$-ray flux is sufficient to generate
the measured event rate that exhibits an annual modulation.
