Investigations of the effect of a rocking motion on the seismic response of liquid storage tanks started in 1980 by Ishida . Later, in 1985, Haroun and Ellaithy  presented an analytical mechanical model for flexible cylindrical tanks undergoing both a lateral translation and a rigid base rocking motion. Using a classical hydrodynamic pressure approach and assuming an approximate deflected shape for the tank walls, explicit expressions for parameters of the model were obtained. In addition, they investigated the effect of large deflections on the dynamic response of flexible tanks. Veletsos et al  analyzed the dynamic response of upright circular cylindrical tanks to a rocking base motion of an arbitrary temporal variation. He generalized the mechanical model for laterally excited tanks to include the effects of base rocking of both rigid and flexible tanks.
The response of liquid storage tanks to vertical excitations has not drawn much attention as most studies were concerned with the response due to lateral excitations. Bleich  studied the forced axial response of tanks by idealizing the tank shell as a system of rings stacked on top of one another, but he ignored the axial deformations and bending rigidity of the tank wall. Marchaj  conducted a simplified study that focused attention on the importance of the vertical acceleration in the design of tanks. Kumar  carried out a critical study of axisymmetric seismic behavior of tanks in which the radial motion of partly filled tanks was considered but effects of axial deformations were neglected. He reported that for near full tanks, such approximation has negligible effects on the accuracy of results, but for near empty tanks, axial deformations may influence the response especially for tall tanks. Veletsos and Kumar  presented a design procedure for evaluating the effects of vertical shaking on tanks.
In 1985, Haroun and Tayel  reported on a comprehensive study of effects of the vertical component of a ground excitation. They evaluated the natural frequencies using both numerical and analytical techniques. In their study, they considered both fixed and partly fixed tanks. They calculated tank response under simultaneous action of both vertical and lateral excitations in order to assess the relative importance of the vertical component of a ground acceleration, which has been shown to be important. Rammerstorfer et al  developed an iterative procedure using the added mass concept to obtain the dynamic pressure resulting from a horizontal excitation. They showed that the formula for rigidly based tanks can be used to add the dynamic pressure caused by the vertical excitation. They reported that the stiffness dependent radiational damping causes the maximum dynamic pressure due to the vertical earthquake component to depend essentially on the stiffness of the soil. They discussed three different possibilities for superposing the dynamic pressures due to the horizontal and the vertical earthquake components on the static pressure, and the different modes of wall instabilities.