  The neutron flux at low energy ($E_n\leq15$ MeV) resulting from the
radioactivity of the rock in the underground cavern of the India-based Neutrino
Observatory is estimated using Geant4-based Monte Carlo simulations. The
neutron production rate due to the spontaneous fission of $^{235, 238}$U,
$^{232}$Th and ($\alpha, n$) interactions in the rock is determined employing
the actual rock composition. It is been shown that the total flux is equivalent
to a finite size cylindrical rock ($D=L=140$ cm) element. The energy integrated
neutron flux thus obtained at the centre of the underground tunnel is 2.76
(0.47) $\times 10^{-6}\rm~n ~cm^{-2}~s^{-1}$. The estimated neutron flux is of
the same order ($\sim10^{-6}\rm~n ~cm^{-2}~s^{-1}$)~as measured in other
underground laboratories.
