PURPOSE: To prevent sludge from discharging out of a furnace of a refining container and to get a sludge discharting position inclined angle capable of discharging a maximum amount of slag by a method wherein gas is blown from a tuyere arranged at a refractory inner wall of a refining container and a variation of its back pressure is sensed.

CONSTITUTION: A lower wall at the upper most end of a slag discharging passage of a refining container, for example, a main body 1 of a converter is provided with a tuyere 4 and gas such as argon is blown into the container at its bottom part. A pressure in front of the tuyere is measured by a pressure gauge 5. With such an arrangement as above, a variation of back pressure when molten slag 2 just above the tuyere 4 is changed to molten metal 3 is sensed. Then, the refining container 1 is inclined until an inclination angle θ0 having an inclination angle θ' added with an inclination angle 68 required for causing a surface of the molten metal 3 to reach the uppermost end of the container from the tuyere 4 is attained, the inclination of the container 1 is stopped when the angle θ0 is attained and then the slag 2 overflows. With such an operation as above, the slag can overflow and be discharged without flowing-out of the molten metal.