Both the source and load sides of a power system have randomness. This affects the capacity of the distribution network in accessing distributed power sources. For this reason, a method for evaluating the carrying capacity of distributed generators in a medium voltage distribution network considering the randomness of power sources and loads is proposed. First, the outputs of distributed power sources and loads are decomposed into predictable and stochastic variables, and combined with a sequential Monte Carlo simulation method to simulate the source-load stochastic production model in the time period. Secondly, this paper makes a division of power supply partitions and a simplification of the source-load access location, with the goal of maximizing the capacity of each power supply zone to access distributed power sources and also considering constraints such as transmission capacity, voltage deviation, and short-circuit current to calculate the stochastic power flow with the distribution network hosting capacity model. Then, using the index variation and limit distance as the measurement basis, the multi-distributed power supply orderly access strategy is determined. This prevents the distribution network from being limited in power supply hosting capacity because of inappropriate local operating parameters. Finally, the model is applied to a regional distribution network in a central city to verify the feasibility and effectiveness of the method.