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This paper is concerned with modeling the time-varying underwater acoustic channel especially when its time variability is induced by transmitter and/or receiver motion. The relative motion between transmitter and receiver creates a Doppler shift of the received signal and introduces a time-scale variation to the channel which is characterized by Doppler spread and channel coherence time. In order to simulate the physically probable time-varying channel, we suggest a channel model which is based on the ray theory. It exploits the eigen-ray information of ray tracing to determine the discrete signal transmission paths and adds them to random diffusive multipaths whose amplitude and phase are modeled by Rayleigh and uniform distribution, respectively. If the carrier frequency is quite large, it satisfies the uncorrelated scattering assumption and gives the scattering function which shows how the signal is distributed over range and frequency. We apply the suggested model to a case of an underwater platform moving in the shallow water and present its result.