The security and privacy of underwater acoustic sensor networks has received extensive attention recently due to the proliferation of underwater activities. This paper proposes an analytical model to investigate the eavesdropping attacks in underwater acoustic sensor networks. Our analytical framework considers the impacts of various underwater acoustic channel conditions (such as the acoustic signal frequency, spreading factor and wind speed) and different hydrophones (isotropic hydrophones and array hydrophones) in terms of network nodes and eavesdroppers. We also conduct extensive simulations to evaluate the effectiveness and the accuracy of our proposed model. Empirical results show that our proposed model is quite accurate. In addition, our results also imply that the eavesdropping probability heavily depends on both the underwater acoustic channel conditions and the features of hydrophones.