Abstract: Fracturing process of rock caused by loading is an important problem in study of failure mechanism of rock. In order to analyze quantitatively the fracturing process of rock, sandstone specimen was tested under uniaxial and triaxial compressions and observed by X-ray . From the result the formula of rock damage variable and its increment and the calculation of rock initial damage variable are proposed. Analyzed CT images and relational curves between stress and density damage increment of sandstone, we found that the fracturing process of sandstone occurred in five stages,i.e. the compaction by initial damage, crack extension, the crack merging and forking of crack, the continuos forking and extension of crack, and the connection of cracks and failure of rock. In the stage of compaction by initial damage, density damage increment of sandstone is positive and the rate ia positive. In the stage of crack extension, local density damage increment of sandstone decreased and changed from positive to negative, and the rates changed also from positive to negative with increasing stress. In the stage of merging and forking of crack, density damage increment of sandstone is negative and the rate became higher. In the stage of continuous forking and extension of crack, density damage increment of sandstone is continuously negative, but the rate became slower. In the stage of connection of cracks and failure of rock, the density damage increment of sandstone is continuously negative and the rate became higher.