Tensile, shear strength and other forms of damages, even buckling failure in local compression zones will happen to buried pipelines under the action of ground permanent large deformation caused by normal fault movement. We used ABAQUS software to establish a three-dimensional pipe-soil interaction model under the ground permanent deformation, adopted nonlinear contact method to simulate the pipeline-soil interaction, and analyzed the influence of different pipe-diameters and crossing angles on the failure mode. By analyzing some examples, it is showed that tensile strength damage is prone to happen to small-diameter pipelines, while buckling failure to thin-wall large-diameter pipelines, and the critical value of pipe-diameter from intensity damage to buckling failure is 0.65 m. When crossing angle is bigger than 90°, the bigger the angle is, the easier buckling failure happens. And the critical value of crossing angle from intensity damage to buckling failure is 100°.