Elephant-foot buckling, characterised by an axisymmetric shell bulging adjacent to the base support, constitutes one of the main modes of failure in seismically-excited steel tanks and in most cases results in loss of tank contents due to weld or piping connection damage or may lead to total collapse of the tank. Current design codes deal with this mode of failure as a buckling failure and hence calculate an allowable buckling stress and compare it to the axial stress in the shell. Recent earthquake incidents have shown a compelling need to revise these codes. In this paper, an analytical study is performed using non-linear finite element modelling to investigate this mode of failure. A quasi-static hydrodynamic load is applied to the tank walls simulating the effect of the accelerated contained liquid. The elephant-foot buckling phenomenon was shown to correlate closely with the yielding of the steel shell as indicated by the Von Mises stress. A new design methodology is introduced using the Von Mises stress and an example is presented to illustrate this approach. A detailed analysis is also presented to estimate the location of the elephant-foot bulging failure for existing tanks which could serve as an aid in the process of repairing these tanks.