Neutron monitors (NMs) are ground-based detectors that are widely used to detect secondary particles produced by the collisions of primary cosmic rays (CRs) and air molecules in the Earth’s atmosphere. Bare neutron counters (BCs), operated without the lead producer and polyethylene reflector, are more sensitive to CRs of lower energy. Thus the ratio of BC to NM enhancements has proven useful for determining the spectral index of relativistic solar particles during ground level enhancements. Recently, a unique array of 6 BCs has been installed along with the 18- counter NM at the Cosmic Ray Laboratory at Mawson Station, Antarctica. The BCs are placed at different locations relative to the laboratory wall and the NM, allowing measurements of the effect of the surrounding environment on the BC response and validation of Monte Carlo (MC) simulation techniques. We use the FLUKA software to simulate atmospheric CR interactions above the station and investigate the NM and position-dependent BC yield functions at Mawson. The results show that secondary neutrons produced in the environment over 1 kilometer away can affect the BC yield function. The results will provide a better understanding of the yield functions, their position dependence, and the use of the BC to NM ratios to determine the spectral index of relativistic solar particles.