Humpback whales Megaptera novaeangliae are an endangered species of mysticete (baleen) whale. Their cosmopolitan, coastal habitat places them in strong potential conflict with human activity such as net entanglement, vessel collisions, or harassment by anthropogenic sound. Contemporary interest in the potential impact of anthropogenic sound on marine mammals, combined with legal requirements for protection of these species, has led to intense research focus on how marine mammals use sound, and how sound may harass or harm these animals. Baleen whales such as humpbacks are focal species because their vocalisations are very low in frequency, suggesting that these whales may be most susceptible to harassment by low-frequency anthropogenic sound. A major obstacle to understanding the potential impact is the paucity of data on hearing sensitivity of mysticetes. In this paper, we address this issue with a novel, unique computational model of humpback whale auditory sensitivity. The model is based upon parameters derived for bottlenose dolphins Tursiops truncatus, the cetacean whose auditory systems are best understood. One set of model parameters was derived from comparative morphometric and sensorineural analyses of terrestrial and marine mammal ears. A second set was derived from psychophysical experiments with bottlenose dolphins. The parameters were combined to produce a model of frequency range, relative sensitivity, and underlying auditory filter shapes for humpback whales. We present the model and discuss its application to understanding the potential impact of anthropogenic sound on this species [Project CS-1082 of the Strategic Environmental Research and Development Program].