Equations previously developed for a ground-supported, rigid cylindrical reservoir and based on the classical approximations
of linearized, inviscid wave mechanics are extended to cope
with the case of elevated reservoirs supported by flexible columns. Solutions for column shear forces and free surface displacements are developed in a form suitable for computer prediction of time-history response. Sensitivity of results to the time-step size and the number of slosh modes is examined, and it is concluded
that accurate estimates of water level fluctuations can only be obtained if at least 10 modes are used. A realistic example is presented to illustrate the method, and the response to two accelerograms is compared with predictions obtained from Housner's simplified approach.