The present study analyzes flexible rectangular concrete base-isolated liquid storage tanks (LSTs) for bi-directional earthquakes. The base-isolated LST is modeled in ABAQUS finite element software. The liquid is modeled by the Equation of State (EoS) with arbitrary Lagrangian-Eulerian (ALE) remeshing algorithm, whereas the hexahedral solid finite elements model LST. Nonlinear time history analysis is performed by considering the LSTs' material nonlinearity and the nonlinearity produced in LST due to the water-structure interaction. As illustrative examples, different LSTs are considered in the present study with five lead rubber bearing (LRB) isolators each, four at the corners and one at the center. The parameters varied for analysis are the isolators' effective frequency, peak ground acceleration (PGA), height of water, and aspect ratio of LSTs. The response quantities of interest include Tresca stress, sloshing height, hydrodynamic pressure, overturning moment, and base shear. The numerical study results show that the liquid's sloshing increases by about 20%-30% at optimum frequency. Still, the forces induced in the tank are considerably reduced. The height of water, and aspect ratio of LSTs significantly influences the response behavior of the isolated tank.