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Abstract In this study, a mathematical model has been designed to calculate the deformation of river bed in its simplest form. The model has been used to simulate the unsteady rlow in open chann eLs , The problem of Upsteady flow is carried out for the one-dimensional flow conditions and then two dimen- sional flow conditions using an implicit difference scheme” Such scheme give s tho possibility to use large,r time step than that used for the explicit scheme. Using the calculated flow parameters? the aedLment transport regime has been studied for the case of suspended load t z-ansport t and then t ransLat ed to get the effect on bed deformations. The basic equations for calculatine the unsteady regi~e were developed on the assumption that the problem could be treated as a. one-dimensional flo”, and then eeneralised to the case of two dimensional flow taking into consideration the var-Lat i on of Ylidth of bed channel. The channel is assumed to have a rectangular section at any location. This mo deL was desi gn ed to calculate the velocities and water levels by changing the differential equations of continuity and mornerrtum Ln t o a difference form. The new |