The simulation of the neutron background for Phase II of the SIMPLE direct dark matter search experiment is fully reported with various improvements relative to previous estimates. The model employs the Monte Carlo MCNP neutron transport code, using
as input a realistic geometry description, measured radioassays and material compositions, and tabulated (alpha,n) yields and spectra. Developments include the accounting of recoil energy distributions, consideration of additional reactions and materials and examination of the relevant (alpha,n) data. A thorough analysis of the simulation results is performed that addresses an increased number of non-statistical uncertainties. The referred omissions are seen to provide a net increase of 13$%$ in the previously-reported background estimates whereas the non-statistical uncertainty rises to 25$%$. The final estimated recoil event rate is 0.372 $pm$ 0.002 (stat.) $pm$ 0.097 (non-stat.) evt/kgd resulting in insignificant changes over the results of the experiment.
