Optimal design of any drilling program requires a good knowledge of the wellbore hydraulics. For conventional mud drilling, established techniques are available for formulating some understanding of the associated wellbore hydraulics but this is not the case for air drilling. It is a fact generally acknowledged that the wellbore hydraulics involved in air drilling presents a distinct problem from those associated with mud drilling. A systematic study of this problem especially utilizing fundamental approach is lacking. This study addresses this important problem using a fundamental hydrodynamic multiphase flow model. The model incorporates the fundamental physics involved in the pneumatic transportation of solid cuttings in the drill string-wellbore annulus. This model forms the basis for a predictive tool for the optimal lifting velocity, an essential ingredient in the optimal design of the air drilling program. Air drilling program design must rely on the a priori knowledge of the basic design parameters such as how much air is required for optimal lifting of the drill cuttings, pressure drop as a function of drilling rate, etc. Drilling engineers often experience frustration due to lack of models with adequate predictive capability to help them answer these basic questions. Available correlations are, at best, gross approximation and more importantly, they fail woefully to account for the physical phenomena that are observed in pneumatic conveying involved in air drilling such as choking, clumping, etc. We present a fundamental wellbore hydraulics model based on the understanding of the physics involved in the pneumatic transport of solid cuttings in the the drill-string/wellbore annulus. Extensive parametric analysis of the system is performed to validate the viability of the model as a predictive tool. Its capability as a design and scale-up tool is also investigated by simulating field conditions. The model is demonstrably capable of predicting the pressure drop profile in the annulus under various simulated drilling conditions. In addition, results demonstrate the capability of the model in being able to predict a number of phenomena that are associated with lifting cuttings out of the hole during air drilling. The model possesses scale-up capability.