The rapid development of new energy technologies will make them the main source of power generation in the future. However, the intermittent and fluctuating characteristics of new energy power generation make it highly susceptible to environmental influences. In view of insufficient power supply in urban distribution networks under extreme weather conditions, a power supply restoration strategy considering the regulation capability of flexible resources is proposed. Firstly, air conditioners and electric vehicles, which are typical adjustable flexible resources in urban distribution networks, are modeled, and their regulation capabilities are evaluated. Next, based on the evaluation results, the optimal power supply restoration path is solved to prioritize the power supply to critical loads in the distribution network. Finally, the IEEE 33-bus system proves that this method can quickly identify the optimal restoration path of power supply and effectively reduce the outage rate of critical loads, which is of great significance for improving the resilience of urban distribution networks.