Vector transducers generate or measure signals in the vector components of the acoustic field. Examples of the vector components are acoustic particle velocity and acoustic particle acceleration. In recent years underwater communication schemes using vector projectors as transmitters and vector sensors as receivers have been proposed. Therefore the need for characterization of the vector components of the acoustic field as efficient communication channels has emerged. In this paper we present two vector-field channel models which are suitable for two different multipath shallow water channels. Channel correlations and channel powers are studied in detail for each model, and closed-form expressions are derived in terms of the physical parameters of the channel. The results can serve as useful tools and metrics for communication system design using underwater acoustic vector transducers. They are also useful for estimating channel parameters such as angle spreads, angle of departures or angle of arrivals using vector transducers.