Abstract： To comprehensively evaluate the dynamic stability of liquid storage tanks under earthquake excitations, the equivalent dynamic perturbation equations were established based on coupled fluidsolid model with displacementpressure form, the resistance force in structure domain was parameterized by timevarying geometric stiffening matrix, the generalized perturbation variables were then modified and the vector length was adjusted in real-time, and the dynamic Lyapunov characteristic exponents were then solved with time-stepping techniques, by which the dynamic stability analysis of a 100 000 m3 oil storage tank was respectively executed under harmonic and earthquake ground motions. The results show that the dynamic instability regions obtained by the above Lyapunov method were essentially consistent with the estimates of Floquet method, and the maximum relative error of critical peak ground acceleration calculated by Lyapunov method and B-R criteria method is appoximately 10 %, and the wind girders are helpful to inhibit dynamic instability regions and improve the critical peak ground acceleration. The proposed Lyapunov method is suitable for secondorder dynamic systems, can consider the effect of earthquake duration, and does not restrict the characteristics of seismic waves. Moreover it also dramatically reduces the computing cost of dynamic stability analysis and meets the precision requirement for engineering application.