The integration of large number of photovoltaic power stations into the distribution network increases the operational uncertainty, and have a significant impact on the operational flexibility of the distribution network. This paper first investigates the calculation algorithm which aims at estimating the degree of flexibility that can be provided by the connected point to the main grid, energy storage devices and demand response loads. Then, a bilayer optimal dispatch model of distribution networks with distributed photovoltaic power stations is established with the consideration of the system flexibility. The upperlayer model solves the optimal dispatch scheme that minimizes the distribution network operating cost under a certain scenario of photovoltaic output, while the lowerlayer model solves the most severe scenario within the fluctuation range of photovoltaic output. By the iterative solution of the upperlayer and lowerlayer models, the optimal dispatch scheme of the distribution network is obtained. In addition, although the extreme scenarios merely occur in actual operation, satisfying the flexibility requirements of these scenarios usually requires relatively high economic cost. To address this problem, intuitionistic fuzzy programming is introduced to transform the original optimal dispatch model into an intuitionistic fuzzy programming model, which could obtain a comprehensive optimal dispatch scheme for satisfying the operating costs and flexibility constraints. Finally, an actual distribution network model with distributed photovoltaic is used to validate the correctness and effectiveness of the proposed method.