In order to identify the link criticality in the urban road network, the identification method of critical links in the urban road network based on the satisfied traffic demand rate was proposed. The impact of link failures on travels under different scenarios is studied, and the link criticality was identified and ranked. Firstly, the modeling method of urban road network was introduced, and the failure coefficient of link capacity was introduced to represent the failure degree of links. Then, five existing evaluation indicators were introduced as the reference, the concept and calculation method of satisfied traffic demand rate were proposed based on the concept of travel time budget in the framework of traffic assignment, and the identification method and ranking consistency comparison method of critical links were introduced. Finally, two benchmark networks were used to simulate the identification results of critical links under different scenarios, and the comparative analysis of various indicators were conducted to validate the effectiveness of the proposed method. The results show that the satisfied traffic demand rate is a global network-wide indicator, which can characterize the impact of factors such as traffic demand, link failure severity, and travel time budget on the results of critical link identification. Moreover, its identification results have a strong or very strong positive correlation with the results based on link importance and traffic network efficiency indicator. This study can help traffic managers deepen their understanding of urban road networks and provide theoretical guidance for enhancing the resilience of urban road networks.