The work reported here as applications in neutron detection and 14C dating. In detection, one wants to measure a signal in the presence of the natural neutron background created by primary cosmic ray particles incident on the atmosphere. Neutron sources created by these cosmic rays and resulting fluxes are calculated as a function of depth in air, seawater, ground, iron, and aluminum. What is new here is the analytical generation of cosmic ray neutron sources as a function of depth in various materials. Good agreement is obtained with experimental data for both neutron spectra and fluxes in the air over ground geometry. The air/seawater geometry has the lowest cosmic ray induced interface neutron flux (3.1¿10-3) neutrons/(cm2 s)) followed by air/ground (6.4¿10-3), air/aluminum (2.1¿10-2), and the highest interface value for air/iron (7.7¿10-2) neutrons/(cm2 s)).