Accurate understanding of the subsurface production rate of the radionuclide 39 Ar is necessary for argon dating techniques and noble gas geochemistry of the shallow and the deep Earth, and is also of interest to the WIMP dark matter experimental particle physics community. Our new calculations of subsurface production of neutrons, 21 Ne, and 39 Ar take advantage of the state-of-the-art reliable tools of nuclear physics to obtain reaction cross sections and spectra (TALYS) and to evaluate neutron propagation in rock (MCNP6). We discuss our method and results in relation to previous studies and show the relative importance of various neutron, 21 Ne, and 39 Ar nucleogenic production channels. Uncertainty in nuclear reaction cross sections, which is the major contributor to overall calculation uncertainty, is estimated from variability in existing experimental and library data. Depending on selected rock composition, on the order of 10 7 -10 10 α particles are produced in one kilogram of rock per year (order of 1-10 3 kg −1 s −1 ); the number of produced neutrons is lower by ∼ 6 orders of magnitude, 21 Ne production rate drops by an additional factor of 15-20, and another one order of magnitude or more is dropped in production of 39 Ar. Our calculation yields a nucleogenic 21 Ne/ 4 He production ratio of (4.6 ± 0.6) × 10 −8 in Continental Crust and (4.2 ± 0.5) × 10 −8 in Oceanic Crust and Depleted Mantle. Calculated 39 Ar production rates span a great range from 29 ± 9 atoms kg-rock −1 yr −1 in the K-Th-U-enriched Upper Continental Crust to (2.6±0.8)×10 −4 atoms kg-rock −1 yr −1 in Depleted Upper Mantle. Nucleogenic 39 Ar production exceeds the cosmogenic production below ∼ 700 meters depth and thus, affects radiometric ages of groundwater. The 39 Ar chronometer, which fills in a gap between 3 H and 14 C, is particularly important given the need to tap deep reservoirs of ancient drinking water.