The direct molecular simulation (DMS) method is used to obtain shear viscosity data for non-reacting air and its components by simulating isothermal, plane Poiseuille subsonic flows. Shear viscosity is estimated at several temperatures, from 273 K to 10 000 K, by fitting the DMS velocity profiles using the analytic solution of the Navier–Stokes equations for this simple canonical flow. The ab initio potential energy surfaces (PESs) that describe the various atomic-level interactions are the only input in the simulations. Molecules involved in a collision within the flow can occupy any rovibrational state that is allowed by the effective diatomic potential. For molecular nitrogen, oxygen, and air at standard condition molar composition, the DMS shear viscosity predictions are in excellent agreement with the experimental data that are available up to about 2000 K. The results for pure molecular nitrogen and pure molecular oxygen also agree very well with previously published quasi-classical trajectory (QCT) calculations based on the same PESs. It is further shown that the ab initio shear viscosity data are generally lower than the corresponding values used in popular computational fluid dynamics codes, over a wide temperature range. Finally, Wilke's mixing rule is demonstrated to accurately predict the DMS air viscosity results from the pure molecular components data up to 4000 K.