The stability factors on the single crystal copper continuous casting were researched in this paper. The effects of various process parameters on the surface quality and the solidification structure of the ingot in the continuous casting process of the single crystal copper were systematically studied. The temperature at mold outlet, the flow rate of cooling water, the cooling distance, the melt temperature and the drawing speed were the major factors determined the process of the single crystal copper continuous casting. From the researches of the stability factors on the single crystal copper continuous casting, it is found that these problems of leaking out, water leakage, drawing immobility and abruption play important roles on the stability of continuous casting process. From the researches of the single-crystal copper continuous casting, the effects of various parameters on the surface quality and the solidification structure of the ingot are realized by changing the position and the shape of the solid-liquid interface. The perfect position of the solid-liquid interface is 5mm above the mold outlet and the perfect shape of the solid-liquid interface is umbonate. The specimen of pure Cu, whose surface is bright, is obtained by the method of continuous unidirectional solidification by using the equipment of tow-flow continuous unidirectional solidification in one furnace. The solidification structure is composed of single crystal which is parallel to the axial direction. Then the optimal process parameters determined are that the temperature at mold outlet is 1020℃, the flow rate of cooling water is 1000L/h, the cooling distance is 96mm, the melt temperature is 1450℃and the drawing speed is 14mm/min.