Estimation of seismic vulnerability of existing equipment in petroleum complexes, traditionally has been done by using general fragility curves which have been developed for a group of equipment without considering their physical specifications. Although these kinds of fragility are suitable for preparing emergency plans and governmental decision making, for the sake of seismic upgrading of existing facilities, specific equipment fragilities are needed. In this paper un-anchored steel storage tanks, which is among the most vulnerable equipment in petroleum facilities, are selected for a case study. Probabilistic demand models for Elephant Foot Buckling (EFB) and welding failure at the connection between the bottom plate and shell are developed based on FEM analytical data, and a Bayesian updating rule is used to assess the unknown demand model parameters. The approach properly accounts for both aleatory and epistemic uncertainties. Developed probabilistic demand models are used to estimate the fragility of critical failure modes of selected tanks and real world data. The approach can be applied for other failure modes and other equipment, as well.