Abstract: The proportion of distributed renewable energy generation in distribution network increases year by year, and its uncertainty brings challenges to the safe operation of distribution network. It is important to quantify the impacts of source-load uncertainty on distribution network power flow. Considering the random and fuzzy characteristics of source-load, this paper established a random source-load fuzzy parameter model. Then, an uncertainty quantification method was proposed for distribution network power flow considering the random and fuzzy characteristics of source-load. The proposed method includes two stages: uncertainty representation and sensitivity analysis. In the uncertainty representation stage, a polynomial-chaos-based Kriging (PCK) method was proposed for the efficient calculation of random-fuzzy power flow in distribution network. In the sensitivity analysis stage, the global sensitivity analysis (GSA) method based on membership function was proposed to quantitatively evaluate the impacts of random source-load fuzzy parameters on distribution network power flow and accurately identify the critical parameters. The proposed method was applied in 33-node and 123-node distribution network systems with distributed renewable energy generators. The effectiveness of the proposed methods was verified by simulation results.