A mathematical model for simulating morphological changes in space and time of the 124 km long alluvial reach of the Kosi River based on the data in the period 1968-79 is developed. Equations are obtained to describe the changes of streambed parameters such as minimum bed level, river width and maximum river depth. Fourier sine series are used to fit the river cross-sections over the studied reach for different years. The general trend of a stream cross-section can be modeled satisfactorily with the Fourier sine series. Temporal variations in bed level and width of the river have time periods of about 7year and 3.2-4.3 years, respectively, and are controlled by mean annual discharge with a time period of 13.9 years.