The Stochastic Demand Inventory Routing Problem ( SDIRP) is a typical NP-hard problem and is also the key to implementing Vendor Managed Inventory ( VMI) strategy． This paper analyses the optimal strategies to SDIRP under direct delivery policy，Milk-Run delivery policy without vehicle capacity constraint， and Milk-Run delivery policy with vehicle capacity constraint，respectively．It is proved that ( s，S) policy is the optimal inventory policy for the first two kinds of SDIRP．The third kind of SDIRP can be solved after being transformed into the first two kinds of SDIRP via Fixed Partition Policy ( FPP) ．Then，the properties of the optimal strategies to SDIRP are analyzed，and the lower and upper bound of the parameters for the optimal strategy are given．An algorithm is proposed to solve the first two kinds of SDIRP．Finally，this paper presents a numerical example to analyze the efficiency of the algorithm and discusses the practical application of ( s，S) policy under the fixed route delivery policy．