Predicting the steady state distribution of air pressure in the unsaturated zone resulting from a pneumatic test provides a method for determining air-phase permeability. This technique is analogous to the inverse problem of well hydraulics; however, air flow is more complicated than ground water flow because of air compressibility, the Klinkenberg effect, variations in air density and viscosity that result from temperature fluctuations in the unsaturated zone and the possibility of inducing water movement during the pneumatic test. An analysis of these complicating factors reveals that, when induced water movement can be neglected, a linear version of the airflow equation can provide an appropriate approximation for the purpose of determining air-phase permeability. Two analytical solutions for steady state, two-dimensional, axisymmetric airflow to a single well partially screened in the unsaturated zone are developed. One solution applies where there is a stratum of relatively low air permeability, separating the stratum in which the well is completed, from the atmosphere. The other solution applies where there is no separating stratum between the domain and atmosphere. In both situations the water table forms the lower horizontal boundary. Applications of both solutions to determine air permeability from data collected during pneumatic tests are presented.