New method for handling roof of the base successive mining is proposed, which is induction caving in the roof. The key is that it is made certain to the station of the space-time in the induction caving roof, as the stress is released with the mining process. And applying the catastrophe theory, the influencing factors of induction caving roof are studied in the emptied areas, such as the mechanical property of the surrounding rock, the area of the gob,the scope and dimension of tensile stress. The results show that the key factor is the area of the gob to the method of the induction caving roof. Then according to the geology and the ore characteristic, the three dimension FEM mechanical model is built in Tongkeng Mine, the laws of the tensile stress are analyzed to the space and the time in the roof with the mining, then it is rational design to the mine step and time of the handing the roof.