Stealth and high endurance make submarines ideally suited to a variety of missions, and finding ways to detect, track, and, if necessary, acquire and attack them has long been a topic of research. In this thesis, we study effective ways to operate an MH-60R helicopter in anti-submarine warfare ASW missions. Following an initial cue given by an external source indicating the presence of a possible submarine target, a helicopter is sent to detect, follow, acquire, and attack the submarine. To perform its mission, the helicopter can carry various payloads of sensors and torpedoes. The first part of the thesis focuses on a helicopter equipped with dipping sonar and develops a model that optimizes the operation of the helicopter and measures its effectiveness. We analyze the effect of the different input parameters, such as helicopter speed, submarine speed, sensor detection radius, and travel time to the point of detection on the optimal dipping pattern and the probability of mission success, and show that arrival time is the most important parameter. We also address the optimization problem associated with the payload of a helicopter on an ASW mission and determine the best mix of fuel, sensors, and weapons for a helicopter on such a mission.