A purely physical model for the simulation of cosmic ray particle interactions with the Earth's atmosphere and subsequent production and transport of secondary particles is presented. Neutron and proton spectra as a function of the coordinate in the atmosphere were calculated using a GEANT / MCNP-based code system. The calculated neutron fluxes are in good agreement with experimental data based on neutron monitor measurements. These fluxes, together with experimental or evaluated cross sections, were used to calculate the production rates of ³H, ⁷Be, ¹⁰Be ¹⁴C, and ³⁶Cl. The dependencies of these production rates on solar activity and geomagnetic field intensity were investigated in detail. The obtained production rates agree well with most published experimental and theoretical values. Possible reasons for some differences are discussed.