The stream-bed profile was developed by transfer of surface materials on the slopes. The process in developing the stream-slope was explained by the following mathematical model which was formulated by the application of the theory of stochastic process to the transition probability of soil particles on the slopes. The solution of the model was examined to be applicable to represent the profiles of stream-slope and deposit-surface on sabo dam which was formed by transfer of soil particles in the stream. It was described that the application of the theory of slope development was more appropriate than the application of the Sternberg's law to explain the forming process of longitudinal profile of short stream in moutain. The defferences in the scale and the time of formation between the stream-slope and deposit-surface were recognized to be depended on the magnitudes of the parameters in this model.