PICO is a direct Dark Matter detection experiment installed at SNOLAB searching for WIMPs (Weakly-Interacting Massive Particles) using the superheated liquid technique. A slight perturbation in the liquid, e.g. energy deposited by a recoiling nucleus due to its elastic collision with an incoming neutron, can create a bubble. The neutron-induced bubbles produce a signal indistinguishable from those induced by the WIMPs. Therefore, understanding and predicting the internal and external expected neutron background is fundamental for the success of the experiment. The next generation detector is PICO-500, which is planned to have an active volume of 500 L of C3F8. During the construction of this detector, a very careful screening of the materials allows for the selection of materials containing low amounts of neutron-emitting isotopes. This presentation will focus on the work being done to simulate the expected neutron background in the PICO-500 bubble chamber using Geant4 simulations and the results.