It was seen in Chapter 5 how system nonlinearity affects structural responses. The structure, in most of the cases, is supported on a soil medium that may behave nonlinearly, and this may affect the structural responses to a significant extent under the action of moderate to severe seismic ground motions. Several researchers have studied the influence of material nonlinearity of soil on the responses of a structure in the form of a nonlinear stress-strain relationship, transfer function analysis to obtain effective shear wave velocities in soil, a nonlinear load-displacement relationship, etc. [34-38]. The nonlinearity in the system (e.g. in case of slipping foundations) has been studied in the past [40] in the wavelet domain, extending the technique of equivalent linearization [38]. There is a general approach to model system nonlinearity using a hysteretic force-displacement relationship. However, in doing so to model large deformations, the area under the curve also gets larger, and hence a ‘fat’ hysteresis loop may be considered. In such cases, it is always worth modelling the effect of the hysteresis loop instead of representing the system stiffness by a backbone curve and an equivalent viscous damping mechanism (to represent dissipation of energy). In this chapter, the wavelet analytic technique is used to solve the system dynamics in the case of a tank supported on nonlinear soil. However, to keep things simpler, the force-deformation curve, in this case, is assumed to follow an elasto-perfectly-plastic (EPP) path, and subsequently a methodology for obtaining a nonstationary stochastic seismic response of a storage tank is described.