Atmospheric storage tanks damaged by floods may lead to severe NaTech accident scenarios, and the vulnerability assessment of process equipment suffered by natural events is a crucial point in NaTech risk analysis. In the present study, limit state equations for failure modes of displacement and buckling are introduced based on load-resistance relationships. The parameterized fragility models that can be used in a wide variety of atmospheric unanchored storage tanks and floods have been developed based on logistic regression (LR), and moreover, the models are assessed and validated by receiver operating characteristic (ROC) curves and available accident data in literature. The effects of filling level and density of storaged liquid, the diameter and height of tank, and the inundation height and velocity of flood on the vulnerability of different failure modes are analyzed using fragility curves. Furthermore, fragility magic cubes are first proposed to obtain critical disaster conditions and critical filling levels in different cases. Finally, corresponding quantitative mitigation measures in different stages such as site selection, design, and operation are proposed based on the results of vulnerability assessment.