Purpose: Seismic vulnerability assessment of liquid containing storage tanks is the most vital relevance for industrial plants and society safety to endure damage during impending earthquakes. Because such systems also play an essential role in the public lifeline and also ensure continued use in emergencies. Furthermore, considering that the material contained in individual plants could be hazardous, requisite precautions have paramount importance against undesired leakage. The high internal pressure and axial forces exerted by the liquid in the steel tanks near the tank wall bottom produce elastic–plastic buckling, also known as Elephant’s Foot Buckling (EFB). As far as the authors are aware, no study has been carried out that involves a critical assessment and comparison of IDA and truncated IDA-based EFB failure criterion. This study provides insight into incremental dynamic analysis (IDA) and truncated IDA-based seismic evaluation of cylindrical unanchored steel storage tanks by employing a developed pressure-based surrogate modeling approach. For this purpose, probability-based seismic assessment of a representative sample is considered based on IDA and truncated IDA approaches to identify the potential of the EFB failure and to explore potential enhancements in the sophisticated structural analysis model to prevent the hazardous effects of impending earthquakes. Methods: Due to the significance of industrial plants for public safety and benefit, the structural response evaluation methods for different types of storage tanks have been widely reported. In the literature, the most comprehensive analytical assessment methodology is the IDA approach, in which nonlinear time-history analyses are considered in the finite element analysis model to assess the structural model’s seismic performance. Results: To generate fragility curves, both IDA approaches are employed, taking into consideration and ignoring uncertainty of material properties. The values of the two methods-based fragility curves approach each other as the magnitude of dispersion increases. Conclusion: The two fragility curves give the probability of failures close to each other as the dispersion amount increases while considering the uncertainty of the material properties. In addition, fragility curves generated based on the truncated IDA have been found to give a higher probability of failure, up to 32.5 percent. When compared to the IDA-based fragility curves, the truncated IDA-based fragility curves were found to be on the conservative side.