Offshore pipelines often cross large areas with geomorphological, geological, and tectonic conditions that may pose a variety of geohazards, one of which is the co-seismic slippage of active tectonic faults. Ground movement induced by fault slippage imposes substantial straining on the pipelines, threatening their integrity. This paper presents the results of a series of large-deformation parametric finite element simulations of a partially embedded pipeline resting on a fine-grained seabed and subjected to the differential movement of an active strike-slip tectonic fault. Parametric computations were performed for different values of the angle between fault strike and the pipeline axis, shear strength at the seabed surface, and different contact conditions at the soil-pipeline interface. The pipeline is examined for both pressurized and non-pressurized conditions and for different values of wall thickness and pipeline embedment. The developed strains in the pipeline with the application of fault displacement are determined and compared with appropriate performance criteria for steel pipelines. It was found that the angle at which the pipeline crosses the fault trace is an important parameter. For a range of oblique intersection angles for which the pipeline is subjected to overall compression, pipeline buckling occurs at relatively small fault displacements. For other intersection angle values, local buckling is unlikely due to the pipeline stretching with the fault movement that reduces the compressive stresses. Pipeline safety against strike-slip fault rupture may be substantially improved by simply adjusting the routing at the location of fault crossing.