In this report we model old experimental neutron count distribution data with simulations. Included in the simulations are spontaneous fission induced fission chains and cosmic ray induced neutron signals. The experimental data on highly enriched uranium (HEU) was taken at LLNL at sea level, and on Pu at LANL at 7300 feet in altitude. Cosmic rays can create neutron bursts in high-Z materials, which are enhanced in multiplying Special Nuclear Materials (SNM). For HEU at sea level, comparison between simulations and experimental data show that the largest burst events are initiated by cosmic rays, not by spontaneous fission of 238U. Attempts to quantitatively model the HEU experimental data show that additional contributions from cosmic ray induced neutron background in a concrete room improve the comparison significantly. Cosmic rays interacting with the room create a neutron background that dominates the count rate, and can also initiate fission in HEU; the concrete walls can also shield the highenergy hadrons (protons, neutrons, and pions) that create the largest neutron bursts. For HEU of low multiplication, cosmic rays make it easier to detect HEU, but harder to analyze. For a high multiplication Pu ball, even at altitude, the spontaneous fission-initiated fission chains totally dominate the signal - in this regime cosmic rays are unimportant.