In this conceptual and numerical study, sudden stratospheric warnings (SSW) are identified as catastrophes. A catastrophe is the transition toward a separate new equilibrium after the original stable equilibrium state of a dynamical system terminates as an external parameter changes smoothly and slowly across a critical value. Many qualitative results of some previous modeling studies of SSW are interpreted in light of catastrophe theory. For example, the cutoff amplitudes in wave forcing as functions of initial conditions determined by Holton and Dunkerton are shown to be in the loci of unstable equilibria in a bifurcation diagram. Also the stage of warmest polar temperature represents the peak of the overshooting in a catastrophe. Moreover, the rapid restoration of westerlies corresponds to the return from the overshooting, Basic concepts in catastrophe theory related to SSW-for example, hysteresis, cusp and triggering-are demonstrated in a numerical study using the Holton-Mass model. The trans... Abstract In this conceptual and numerical study, sudden stratospheric warnings (SSW) are identified as catastrophes. A catastrophe is the transition toward a separate new equilibrium after the original stable equilibrium state of a dynamical system terminates as an external parameter changes smoothly and slowly across a critical value. Many qualitative results of some previous modeling studies of SSW are interpreted in light of catastrophe theory. For example, the cutoff amplitudes in wave forcing as functions of initial conditions determined by Holton and Dunkerton are shown to be in the loci of unstable equilibria in a bifurcation diagram. Also the stage of warmest polar temperature represents the peak of the overshooting in a catastrophe. Moreover, the rapid restoration of westerlies corresponds to the return from the overshooting, Basic concepts in catastrophe theory related to SSW-for example, hysteresis, cusp and triggering-are demonstrated in a numerical study using the Holton-Mass model. The trans...