Based on the uniaxial and triaxial compression tests of Three Gorges granites，the crack initiation stress under different confining pressures can be obtained by studying the crack strain curves. The results show that the crack initiation stress changes at the same extent with confining pressure, and is generally located between 25% and 50% of the peak strength. Moreover, the crack initiation criteria and progressive damage model are established, and some beneficial conclusions are drawn. The tension concentration model of elliptic crack can be used to explain cracking mechanism of Three Gorges granite at relatively low confinement, and Three Gorges granite mainly occurs lateral damage in the microfracturing process and exhibits the similar damage evolutionary rule under different confining stress. The damage model can be used to describe the crack propagation process.