This paper defines and studies the multiple-sink shortest path problem (MS-NIP). The MS-NIP corresponds to many real-life problems relating to especially terrorist actions. In the MS-NIP, a network user seeks the shortest path to meet the demands of sink nodes while an interdictor aims to maximize the shortest path of a network user by interdicting the arc(s). In this study, we formulate exact mathematical models of the network user and interdictor for the MS-NIP and apply them on an illustrative example. We test the model depending on the different interdiction budget levels and discuss the obtained results.