Abstract: In the present study, the cracking behavior of three-dimensional ellipsoidal flaws with different sizes and inclination angles (the angle between the loading direction and the tilting direction of the flaw) was simulated based on the extended finite element method. Subsequently, compressibility was introduced to describe the degree of the oblateness of the three-dimensional flaw. Finally, the effects of the compressibility and inclination angle of the three-dimensional flaw on the crack initiation load of the model were discussed. The results show that for the flat ellipsoid flaw models, the crack initiation load decreases and then increases as the inclination angle increases from 0° to 75°. For the sphere-like flaws, the crack initiation load changes slightly with the increase in the inclination angle. The crack initiation load decreases and then increases as the compressibility increases when the inclination angle of the flaw is 0°. As the inclination angle increases to 15°, 30°, 45°, 60° and 75°, the crack initiation load decreases as the compressibility increases.