Wireless sensor networks consist of large number of small, low cost and energy limited sensors which are deployed to monitor many physical parameters such as temperature, pressure, vibration motion. Most of the applications implemented with WSN are vulnerable to attacks that come from outside. Black hole attacks are one of the most dangerous of these attacks. In order to determine the black hole attack, it is necessary to model the system. In this paper, black hole attacks are modeled on cluster-based wireless sensor networks.