With the application of a large number of sensitive loads such as frequency converters and electric relays, voltage sag has become an urgent dynamic power quality issue in distribution networks, especially in modern industrial distribution networks with a high proportion of sensitive loads. In order to effectively evaluate the vulnerability of voltage sag in a distribution network and guide the design of a voltage sag compensation scheme, a method for identifying the vulnerable area of voltage sag in distribution network considering multiple sensitive loads is proposed. This paper first introduces the bus sag identification vector, the line sag identification vector and corresponding judgment criteria. Then the distribution of critical points on each line and the location of critical points in the target distribution network are determined. Secondly, based on the obtained voltage sag region of sensitive loads, a hierarchical model of voltage sag domain of the distribution network considering the overlap effect is derived. In addition, the concept of voltage sag influence degree is thus defined to quantitatively evaluate the vulnerable area of voltage sag in a distribution network. Finally, the rationality and feasibility of the proposed method are verified for voltage sag vulnerable area identification of the IEEE14 bus system. This work is supported by Science and Technology Project of State Grid Corporation of China (No. 52153218000B).