Underwater acoustic (UWA) communications have been widely used but greatly impaired due to the complicated nature of the underwater environment. In order to improve UWA communications, modeling and understanding the UWA channel is indispensable. However, there exist many challenges due to the high uncertainties of the underwater environment and the lack of real-world measurement data. In this work, the capability of reservoir computing and deep learning has been explored for modeling the UWA communication channel accurately using real underwater data collected from a water tank with disturbance and from Lake Tahoe. We leverage the capability of reservoir computing for modeling dynamical systems and provided a data-driven approach to modeling the UWA channel using Echo State Network (ESN). In addition, the potential application of transfer learning to reservoir computing has been examined. Experimental results show that ESN is able to model chaotic UWA channels with better performance compared to popular deep learning models in terms of mean absolute percentage error (MAPE), specifically, ESN has outperformed deep neural network by 2% and as much as 40% in benign and chaotic UWA respectively.