The seismic response of liquid-filled rectangular storage tanks has been investigated using analytical methods, and the finite element method implemented in the general purpose structural analysis computer code SAPIV. The liquid is assumed to be linear-elastic, inviscid and compressible. A displacement-based fluid finite element was employed to allow for the effects of the liquid. The tank is assumed to be subjected to horizontal and vertical components of the 13 March, 1992 Erzincan earthquake in Turkey. Rigid and flexible tank solutions are obtained for the chosen sample tank. The effectiveness of the Lagrangian approach for the seismic design of tanks and the effects of wall flexibility on their dynamic behavior are investigated. Finally, conclusions drawn from this study are presented, and some recommendations are made.