Abstract: Based on the Moore-coulomb yield criterion,taking 3^# single coal seam of Changcun coal mine for example,the crack extension discipline of coal damaged and fractured under the different hydraulic pressure is simulated by FLAC^3D numerical simulation software.The simulation results show that the shear failure is the main type of the coal damage in the process of hydraulic fracturing,and the end area of pressure hole will firstly be damaged.With the increase of the hydraulic fracturing pressure,the fastest extension speed of the crack is along the maximum principal stress direction,and the slowest speed is along the minimum principal stress direction.The crack extension length in the pressure hiatal end area of the vertical direction and the towards direction is almost consistent.The influence of crustal stress is apparently decreased.It is linear relationship between the crack length of the maximum principle stress direction and the hydraulic fracturing pressure.