The dynamic responses of a concrete rectangular liquid storage tank on the surface of rigid soil subjected to three-directional earthquake ground motion are investigated with material nonlinearity taken into consideration. Material nonlinearity in concrete is considered using the concrete damage plasticity model. The hydrodynamic pressure due to earthquake ground motion is considered using a finite-element solution of the governing equation for an inviscid and incompressible ideal fluid with the fluid–structure interaction taken into consideration. It was observed from the dynamic analyses that the effects of material nonlinearity and directionality significantly affect the earthquake responses of the considered system. The relative displacement of the structure increased significantly by the nonlinearity of the material. Inclined cracks due to the increased displacement were observed on the long-sided walls. The hydrodynamic pressure can be reduced significantly by the material nonlinearity and is influenced by the directionality of an earthquake’s ground motion. The base shear and overturning moment due to the hydrodynamic pressure and the resulting impulsive mass and corresponding height for a simplified mass-spring analogy are also affected. Because the directionality was observed to have a significant influence on the peak value of the sloshing height, it must be estimated with the directionality considered.