This paper investigates the effect of the multi-directional components of ground motion on an unanchored steel storage tank. Both the liquid sloshing effect and contact behavior between the foundation and tank are included in the study. A three-dimensional model for a foundation–structure–liquid system is numerically simulated using the finite element method. The Lagrange fluid finite element method (FEM) in ANSYS is used to consider the liquid–solid interaction. In the liquid–structure–foundation interaction model, the contact and target elements are adapted to simulate the nonlinear uplift and slip effects between the tank and the foundation. Three earthquake ground motions are selected for evaluating the seismic behavior of the tank. Comparisons are made on the horizontal displacement, “elephant-foot” deformation, stress, base shear and moment, sloshing of the liquid, uplift, as well as slip behavior under the application of the unidirectional, bi-directional and tri-directional components. Under the selected ground motions, the horizontal bi-directional seismic component has great influence on the liquid sloshing in the tank studied in this paper. The vertical seismic component produces high compressive axial stress, and it also makes the uplift and slide of the tank bottom increase significantly. The applicability of this conclusion should be carefully considered when applied to other types of ground motion inputs.