Cooling towers are typical high-rise thin-walled structures which are of hyperbolic rotating shell structure type and significantly sensitive to wind loads. Wind-related local instability is the key control factor in the design of structural geometric shape and tower shell thickness optimization. In fact, this kind of stability analysis has only conducted aiming at normal climate (such as monsoon, etc.) under the guideline of series of national Codes. In order to deal with the issues under disaster climate, physical and numerical investigation to evaluate local stability performance of a super large cooling tower (SLCT) under tornado environments based on Buckling Stress State (BSS) method is implemented. Besides, whole process elastic–plastic collapse simulation of the SLCT exposed to the tornados was also carried out to study the failure mechanism and re-evaluated the reasonability of the well-accepted BSS method for structural wind-resistant design. The results revealed that the tornados would have obvious adverse effects on the structural local stability when the SLCT is located at the tornado vortex core radius compared with those under traditional synoptic winds. The swirl ratios and the central distances between the SLCT and the tornado vortex core have significant effects on the local instability of the SLCT. The extended elastic–plastic collapse simulation discovered that the position of the first crack during SLCT collapse process is basically consistent with the critical position from the elastic local stability analysis of the SLCT, indicating that strengthening measures can be carried out in advance at the critical position for structural local stability improvement under tornado conditions. Besides, the extended elastic–plastic collapse numerical simulation of the SLCT could be as the effective supplement to the structural elastic stability assessment (such as BSS method) in the wind-resistant design of the SLCT.