New models have been computed for the Lunar Prospector (LP) thermal and epithermal neutron counting rates using the particle transport code MCNPX. This work improves upon previous studies by using one code to model the neutron production, transport, and detection processes, and by examining the sensitivity of epithermal neutrons to elements other than hydrogen. Our modeling results for standard anhydrous lunar soils show that when hydrogen is not included in a soil, epithermal neutrons are most sensitive to variations in the abundances of Fe, Gd, and Sm, which is consistent with measured epithermal neutron data. We use our current modeling results, in conjunction with known mineral compositions of lunar soils and other lunar global data sets to conclude that the best explanation for a decrease in the counting rate of epithermal neutrons near both lunar poles is the presence of hydrogen. We have further concluded that the average hydrogen abundance near both lunar poles is 100--150 ppm and is likely buried by 10 ¿ 5 cm of dry lunar soil, a result that is consistent with previous studies. The localized hydrogen abundance for small (<20 km) areas of permanently shaded regions remains highly uncertain and could range from 200 ppm H up to 40 wt% H2O in some isolated regions.