The purpose of this paper is to establish the existence of the critical condition of borehole stability during air drilling. Rock Failure Process Analysis Code2D was used to set up a damage model of the borehole excavated in strain-softening rock. Damage evolution around the borehole was studied by tracking acoustic emission. The study indicates that excavation damaged zone (EDZ) is formed around borehole because of stress concentration after the borehole is excavated. There is a critical condition for borehole stability; the borehole will collapse when the critical damage condition is reached. The critical condition of underground excavation exists not only in elastic and ideal plastic material but in strain-softening material as well. The research is helpful to developing an evaluation method of borehole stability during air drilling.