Aerodynamic tunneling is the process of transporting a vehicle from terrestrial point A to B via a closed tube containing an atmosphere more aerodynamically favorable than air. Equations are derived for "gas efficacy," Gamma, a measure of how well a gas increases Mach-1 speed or decreases drag of a vehicle. Theoretical results, Gamma(p) and its Mach-normalized form Gamma(1), based on reducing the vehicle to a flat plate, allows efficacy to be calculated ab initio as a function of only four gas parameters: ratio of specific heats, pressure, density, and viscosity. Hydrogen has the highest normalized gas efficacy (Gamma(1) = 48.5 s/kg). Ammonia, hydrocarbon gases, and helium have above-average efficacies. Xenon has the lowest (10.1 s/kg). Binary mixtures of hydrogen and methane (or natural gas) are proposed for lowering the upper flammability limit at a relatively small penalty in efficacy. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.