Natural hazard events that trigger technical emergencies (Natech events), as a typical type of multi-hazard, have become a matter of growing concern. In particular, the occurrence of Natech events in industrial areas triggered a number of severe accidents. The present research aims at introducing a sound but simplified methodology to quickly and flexibly assess the vulnerability of atmospheric storage tanks to multiple natural disasters in Natech events. This method consists of 8 steps, relying on the simplified physical models of tank damage caused by natural disasters. The models of wind overturning tank and tank buckling caused by hail are proposed. In addition, the assessment process of tank vulnerability is demonstrated from two aspects: deterministic analysis and probabilistic analysis. The uncertain parameter set (UPS) proposed in the method and the Monte Carlo simulation method can help to purposefully analyze the impact of various parameters and this method is also a general method, which is also applicable to Natech events including other natural disasters or other types of storage tanks.