Abstract: The stability of large-scale hyperbolic shells under wind loads is one of key control factors during structural design. In order to evaluate the local stability of hyperbolic shell structures under the combined action of wind load and other loads, the current codes usually adopt the local stability check formula proposed by Mungan, based on the stress-measured model test considering uniform hydrostatic pressure in 1970s, which also known as Buckling Stress State (BSS) approach. In order to investigate the applicability and rationality of the algorithm while facing to the current development of super-large cooling towers. Based on the structural finite element method, the revisiting analysis aiming at earlier physical models was conducted to validate the existing stability check formula. Then series of calculations involving 21 types of hyperbolic shell cooling tower structures were implemented to clarify the difference between the circumferential fluctuating wind pressure distribution and the uniform pressure distribution of wind-induced internal forces. Under the condition of the wind pressure ultimate load, an updated formula for the critical circumferential stress is proposed. Furthermore, the updated local stability check formula is fitted for engineering practice. The investigation shows that the existing local stability formula of the hyperbolic shell structure from various loading codes cannot deal with 3D non-uniform wind pressure actions. It is recommended to use the updated formula to account complex wind load distributions.