PROBLEM TO BE SOLVED: To prevent segregation, particularly when the density at the center part is enhanced simultaneously, and to obtain a uniform strand (cast slab) over the cross section of the strand by using the drawing force of the strand as the control value for adjusting the position at the tip part of an unsolidified part in the case slab while comparing the position of roll pair, and also a gap between the rolls. SOLUTION: As an actual value, a rolling reduction force P in the prescribed roll pair 23 in the deforming gap of the roll pair 23 executing a deformed section, a deformed thickness ΔD and the strand drawing force Z obtd. depending on a material characteristic value, are set, and the necessary toque to the following driving roll 22 is calculated. At this time, the reference value is the drawing force obtd., when the tip part S of the molten metal or the end part of the solidification directly exists in the gap of the rolls 24, 25. In the deviation between the actual value and the reference value, the correction of the positional relation between the roll pair 23 and the tip part S of the molten metal is executed with the change in casting speed or the change of the position of the roll pair 23.