In order to reveal the physical mechanism of air hammer drilling process, using the finite element methods (FEM), a three-dimensional (3D) contact model of full-scale bit, full-scale teeth and rock is established by using free meshing method. We use a Mohr-Coulomb type material model to describe when and how rock fails, and a triangular wave to replace the stress wave. Using the finite element analysis software (ANSYS), the 3D contact analysis of the bit, teeth and rock is carried out. The results show that: aggressive tensile failure may be primarily responsible for rock breakage in air hammer drilling, while compressive failure (or shear failure) may only contribute as a minor player; the distribution of the fragmentation dents can be used to verify the rationality of tooth arrangement; the larger tooth-hole stress of the outside rows mainly responses for the bit failure, while the larger tooth stress of the inside rows contributes as a secondary factor. The results are further calibrated with a series of field applications and research results.