Liquid storage tanks are vital and have great importance in industrial facilities. One of the best ways to protect the fluid storage tanks against earthquake forces is the use of seismic isolation systems. These systems protect such structures against possible damage during an earthquake by allowing acceptable displacements at the base of the superstructures while preventing the superstructure from entering the nonlinear phases. One of the common methods for computer modeling of these structures is the use of equivalent mechanical models. It should be noted that, the mentioned equivalent mechanical models, are suggested for design of tanks by Standards and Codes. However, they are appropriate for rigid-wall tanks. On the other hand, the recent studies show that the seismic response of a rigid tank may be considerably less than that of a similar flexible tank. In this study, by using a state-of-the-art equivalent mechanical model of cylindrical concrete containers, that considers the issue of wall flexibility, the seismic responses of ground-supported and elevated concrete containers affected by the bi-directional horizontal motion of the earthquake is investigated. The results show that, by selecting the best mechanical properties of seismic base isolation systems, the seismic responses of these tanks can be greatly improved.