The occurrence condition of debris fiow due to rainfall is given by solving the equations for fiow on a slope. The solution shows that a debris fiow will occur on a slope when the accumulated rainfall within the time of concentration exceeds a certain value determined by the properties of the slope. To estimate this critical value, the system analysis technique would be commendable. In this study, a procedure to fine the critical rainfall from the rainfall data whith and without debris flows is proposed. Reliability of this method is verified by applying to the debris flows in Unzen Volcano which recently began to erupt. Discharge of debris flow in a stream is obtained by solving the equation of continuity using the kinematic wave theory and assuming the cross sectional area to be a function of discharge. The computed hydrographs agree weel with the ones observed at the rivers in Sakurajima and Unzen Volcanos. It is found from the derived equation that the runoff intensity of debris flow is in proportion to the rainfall intensity and accumulated rainfall, jointly. This gives a theoretical basis to the conventional method which has been widely used.