The socioeconomic and environmental impact, in case of severe damage on Natural Gas (NG) pipeline networks, highlights the importance of a rational assessment of the structural integrity of this infrastructure against seismic hazards. Up to date, this assessment is mainly performed by implementing empirical fragility relations, while a limited number of analytical fragility curves have also been proposed recently. The critical review of available fragility relations for the assessment of buried pipelines under seismically-induced transient ground deformations, presented in the first part of this paper, highlighted the need for further investigation of the seismic vulnerability of NG pipeline networks, by employing analytical methodologies, capable of simulating effectively distinct damage modes of this infrastructure. In this part of the paper, alternative methods for the analytical evaluation of the seismic vulnerability of buried steel NG pipelines are presented. The discussion focuses on methods that may appropriately simulate buckling failures of buried steel NG pipelines since these constitute critical damage modes for the structural integrity of this infrastructure, when subjected to seismically-induced transient ground deformations. Salient parameters that control the seismic response and vulnerability of buried pressurized steel pipelines and therefore should be considered by the relevant analytical methods, such as the operational pressure of the pipeline, the geometric imperfections of the pipeline walls, the trench backfill properties, the site characteristics and the spatial variability of the seismic ground motion along the pipeline axis, are thoroughly discussed. Finally, a new approach for the assessment of buried steel NG pipelines against seismically-induced buckling failures is introduced. Through the discussion, recent advancements in the field are highlighted, whilst acknowledged gaps are identified, providing recommendations for future research.