The crack initiation stress (CI), a threshold stress at which brittle rock starts to become damaged during compression, has been widely studied. It can be used to estimate the spalling strength of tunnels in brittle rock masses. Many methods based on stress–strain curves and acoustic emission data have been proposed to identify the CI, and these methods have good statistical consistency. In the present study, the influence of varying the Poisson's ratio on the value of the CI is analyzed using the crack volumetric strain (CVS) method, and the physical meaning of the lateral strain response (LSR) method is explained. Based on the LSR method, a more stable lateral strain interval response (LSIR) method is proposed to determine the CI. We analyzed the CI of granite samples from two deep boreholes in the Beishan area, the site of China’s underground research laboratory (URL). The results show that the mean CI values determined by our proposed method are in good agreement with the results from the LSR method. The standard deviation and correlation analysis show that the CI values obtained by the proposed method have a smaller dispersion and a higher independence than those from the LSR method.