To adapt to the future power distribution mode of AC/DC hybrid distribution network and address the lack of operational flexibility adjustment caused by the uncertainty of renewable energy, a two-stage distributionally robust optimization operation model for AC/DC hybrid distribution networks considering flexibility is proposed. Firstly, under the framework of AC/DC hybrid distribution network, the supply and demand relationship of flexible resources is analyzed, and the upward/downward flexibility evaluation index is defined. Secondly, considering various constraints in the system, an optimal operation model describing the economy, renewable energy consumption, and flexibility of the distribution network is constructed. Combined with data-driven typical wind and solar scenarios, a distributionally robust optimization method based on the comprehensive norm distance is adopted to deal with the uncertainty of wind and solar power output. And a two-stage distributionally robust optimization operation model is constructed according to the output characteristics of optimization variables. Finally, convex transformation and solution of the model are carried out, and the validity of the model is verified through a modified 33-node AC/DC hybrid distribution network.