The safety of buried pipeline systems is seriously threatened by earthquake hazards like seismic-induced landslides, lateral spreading due to soil liquefaction and faulting, highlighting the need to accurately evaluate their structural performance in the engineering design practice. Currently, two main finite element modelling approaches are employed for assessing the seismic response of the system accounting for the soil-pipe interaction, such as the simplistic beam on Winkler foundation and the more complex continuum model. While the former is incapable to model the realistic soil-pipeline interaction for large scale deformations and to capture the pipeline local instabilities, the latter presents significant disadvantages in terms of elevated computational demands and required expertise of the operator. In this paper, the seismic performance of a straight buried steel pipeline subjected to strike-slip faulting is analysed within the finite element method, using the beam on Winkler foundation and the continuum approach. To optimize the computational costs, each end of a limited pipe segment crossing the fault is connected to an equivalent-boundary spring, representing the interaction with the rest of the soil-pipeline system. The effect of different soil and pipe parameters having a critical role on the pipeline response is carefully investigated, such as the fault inclination angle, the pipeline burial depth, the soil material, the pipe thickness and the internal pressure. The numerical results obtained using both modelling techniques are accurately compared between each other as well as recent research work in the field, giving a better insight on the mechanical behaviour of the soil-pipeline system under strike-slip movement. Finally, a series of recommendations are proposed to enhance the seismic design of buried steel pipelines crossing active faults suggesting different measures in order to optimize the structural performance of the pipeline against similar environmental hazards.