The inventory in the transfer center of a distribution network plays a key role in meeting customer demands. This study focuses on evaluating the system reliability of a stochastic flow distribution network (SFDN) with inventory. An SFDN is composed of nodes and routes, where each node denotes a vendor, transfer center, or market and each route connects a pair of nodes. Along each route, there is a carrier whose available capacity is stochastic. Different from previous issues regarding system reliability, this study consider that market demand should be met by transfer centers firstly. If the market demand cannot be met by the transfer centers, then vendors must meet the remaining demand to satisfy the market. An algorithm is developed in terms of minimal paths to evaluate system reliability, which is defined as the probability that the SFDN can satisfy the market demand by using inventory from multiple vendors and transfer centers to the market under budget constraints. A numerical example is given to illustrate this proposed algorithm.