A typical viable technique to decrease the seismic response of liquid storage tanks is to isolate them at the base. Base-isolation systems are an efficient and feasible solution to reduce the vulnerability of structures in high seismic risk zones. Nevertheless, when liquid storage tanks are under long-period shaking, the base-isolation systems could have different impacts. These kinds of earthquakes can damage the tanks readily. Hence, the seismic behaviour and vibration of cylindrical liquid storage tanks, subjected to earthquakes, is of paramount importance, and it is investigated in this paper. The Finite Element Method is used to evaluate seismic response in addition to the reduction of excessive liquid sloshing in the tank when subjected to the long-period ground motion. The non-linear stress-strain behaviour pertaining to polymers and rubbers is implemented while non-linear contact elements are employed to describe the 3-D surface-to-surface contact. Therefore, Nonlinear Procedures are used to investigate the fluid-structure interactions (FSI) between liquid and the tank wall while there is incompressible liquid. Part I, examines the effect of the flexibility of the isolation system and the tank aspect ratio (height to radius) on the tank wall radial displacements of the tank wall and the liquid sloshing heights. Maximum stress and base shear force for various aspect ratios and different base-isolators, which are subjected to three seismic conditions, will be discussed in Part II. It is shown that the composite-base isolator is much more effective than other isolators due to its high flexibility and strength combined. Moreover, the base isolators may decrease the maximum level pertaining to radial displacement.