PURPOSE: To execute a continuous casting operation while minimizing the variation of the fluidity of molten steel and preventing the inclusion defect by giving the gradient in the variation of magnetic flux density particularly at the time of putting on and off the electromagnetic brake.

CONSTITUTION: A method for controlling the fluidity of the molten steel in a mold is the method for obtaining a good quality cast slab by controlling while acting the electromagnetic brake force to the discharging stream 3 of the molten steel with static magnetic field 40 and giving the gradient of at least 0.1T/min the variation of the magnetic flux density at the time of changing the magnetic flux density with the static magnetic field 40.