A logistics distribution network is modeled as multi-state flow network model, and based on the assumption that the inventory in distribution centers is given priority to supply the market and the transportation cost has a limit, network reliability refers to the probability that the commodities transported to a certain market can meet the demand and the total transportation cost does not exceed the given limit. According to the relationship between distribution center inventory and market demand, a reliability evaluation method based on minimal capacity vectors is proposed. The reliability evaluation method is verified by example analysis, and the influence of different inventory combinations on network reliability is analyzed.