In this research a mathematical model was developed to study bed elevation variation of alluvial rivers. It utilizes two principal modules of hydraulics and sediment transport for simulation purposes. SDAR (Scour and Deposition model of Alluvial Rivers) is a new model with both one and semi-two dimensional (S-2D) computational schemes. It is regarded S-2D in a sence that lateral variation of velocity, hydraulic stresses, and geometrical specifications are achieved by dividing the main channel into serveral stream tubes. In order to overcome the existing limitations, a new idea of reachwise stream tube concept was also introduced. This allows to include branch connections and withdrawal points across the tube barriers. Sediment routing and bed variation calculations are accomplished along each river strip desigated by virtual interfaces of the tubes. Presently, quasi-steady gradually varied flows are processed by the model. It should also be emphasised that this version is only valid for alluvial rivers composed of noncohesive bed material. To assess the model, several river cases and laboratory data base were used. During calibration runs, the ability of model in longitudinal and transversal bed profile simulation and armor layer development predection were especially detected. Results of simulation are also compared with the results of well-known models, e.g. HEC-6, GSTARS-2, and FLUVIAL-I2. It was found that the ability of model in simulating bed variation is noticeably increased when S-2D concept is introduced. Indeed, the comparative validity tests confirm SDAR"s promising functioning in facing with complex real engineering cases. Obviously more article discussions would bring oppurtunities to demonestrate it"s technical cappabilities profoundaly.