The neutron flux at low energy (E n ≤ 15 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 (α, n) interactions in the rock is determined employing the actual rock composition. It is 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 center of the underground tunnel is 2.76 (0.47) ×10 −6 n cm −2 s −1 . The estimated neutron flux is of the same order (∼ 10 −6 n cm −2 s −1 ) as measured in other underground laboratories.