The SIMPLE project looks for nuclear recoil events generated by rare dark matter scattering interactions. Nuclear recoils are also produced by more prevalent cosmogenic neutron interactions. While the rock overburden shields against (μ,n) neutrons to below 10−8 cm−2 s−1, it itself contributes via radio-impurities. Additional shielding of these is similar, both suppressing and contributing neutrons. We report on the Monte Carlo (MCNP) estimation of the on-detector neutron backgrounds for the SIMPLE experiment located in the GESA facility of the Laboratoire Souterrain à Bas Bruit, and its use in defining additional shielding for measurements which have led to a reduction in the extrinsic neutron background to ∼ 5 × 10−3 evts/kgd. The calculated event rate induced by the neutron background is ∼ 0,3 evts/kgd, with a dominant contribution from the detector container.