The seismic vulnerability of aboveground steel storage tanks has been dramatically proved during the latest seismic events, which demonstrates the need for reliable numerical models for vulnerability and risk assessments of storage facilities. While for anchored aboveground tanks, simplified models are nowadays available and mostly used for the seismic vulnerability assessment, in the case of unanchored tanks, the scientific community is still working on numerical models capable of reliably predicting the nonlinearity due to uplift and sliding mechanisms. In this paper, a surrogate model based on a Kriging approach is proposed for a case study of an unanchored tank, whose calibration is performed on a three-dimensional finite element (3D FE) model using a reliable design of experiments (DOE) method. The verification of the 3D FE model is also done through a shaking table campaign. The outcomes show the effectiveness of the proposed model to build fragility curves at a low computational cost of the critical damage state of the tank, i.e., the plastic rotation of the shell-to-bottom joint.