Crack initiation is related to the behavior of the preexisting microcracks within a rock specimen, which suggests the specimen starts to fail. The determination of crack initiation stress is important for identifying the elastic stage and related mechanical parameters. Uniaxial compression tests with acoustic emission monitoring were performed to study crack initiation for tight sandstone, loose sandstone, and granite. The evolution of the cracking mode, i.e., the statistics of the cracking mode under compression, was obtained through modified acoustic emission parameter analysis. Based on the logarithm of the acoustic emission parameter (LAEP), a cracking mode analysis (CMA) method is proposed and used to determine the crack initiation stress. Results from the tests indicate that the crack initiation stress between the same rock specimens obtained by CMA is very close. The mean ratio of crack initiation stress to compression strength is 0.45, 0.34, and 0.35 for tight sandstone, loose sandstone, and granite, respectively. According to the results of CMA, crack volumetric strain (CVS) method, and lateral strain response (LSR) method, there is no big difference among those methods in tight sandstone and loose sandstone. In granite, the results obtained by CMA are close to those obtained by CVS, but smaller than those obtained by LSR. The CMA interprets the initiation of cracks from the fracture behavior of microcracks and is an objective method to determine the initiation stress.