Long-distance offshore pipelines often inevitably pass through seismic faults that may threaten pipeline safety. A buckling analysis was conducted on offshore buried pipelines crossing active strike-slip faults using nonlinear VFIFE shell elements and modified soil springs. With respect to practical pipeline performance criteria, deformation responses under three scenarios are examined, including the seismic response with different initial pressure conditions, post-earthquake recondition for pressurized pipelines, and post-earthquake resumption for unpressurized pipelines. The results have showed multi-failure modes, including over bending with excessive tensile strain, over bending with obvious depression deformation on the compressive side of the bends, and sequential local collapses accompanied by buckling propagation along the pipeline. For pressurized pipelines, the post-earthquake recondition has a compression effect and leads to greater sectional distortions, even local collapse accompanied by buckling propagation. For pipelines with the maximum flattening parameter smaller than 15.00% at zero-pressure, critical points of the first local collapse have a linear distribution. For unpressurized pipelines, the post-earthquake resumption improves the sectional deformation but intensifies the axial tensile strain. An unpressurized pipeline with a local collapse gains a V-shape dent during the final pressurization. The results are useful for developing performance-based seismic design methodologies for offshore pipelines.