Underwater acoustic communication (UAC) system designers tend to transmit as much information as possible, per unit of time, at as low as possible error rate. It is a particularly difficult task in a shallow underwater channel in which the signal suffers from strong time dispersion due to multipath propagation and refraction phenomena. The direct-sequence spread spectrum technique (DSSS) applied successfully in the latest standards of wireless communications, gives the chance of reliable data transmission with an acceptable error rate in a shallow underwater channel. It utilizes pseudo-random sequences to modulate data signals, and thus increases the transmitted signal resilience against the inter symbol interference (ISI) caused by multipath propagation. This paper presents the results of simulation tests of DSSS data transmission with the use of different UAC channel models using binary spreading sequences.