PURPOSE: To smoothly discharge the remaining molten steel and molten steel slag in a tundish and to prevent the heat radiation during the waiting time till using in the following casting and increase of inclusion in a cast slab caused by the above remaining material, in the tundish being suitable to hot continuous operation.

CONSTITUTION: In the tundish 2 for continuous casting arranging a discharging hole 4 for molten steel and molten steel slag (remaining material) at the upper end edge part, this discharging hole 4 is arranged at the upper edge part of the tundish wall 2a in the parallel surface of the tilting shaft 12 of the tundish 2. A closing cover 5 is arranged and also, the discharging hole 4 is formed as a step-state having a low step at the outlet side 4a of the bed part in the inner wall and a high step at the deep side 4b. At the time of discharging the remaining material 1 from the discharging hole by tilting the tundish, the flow-out locus of the remaining material 1 separated from the deep side front end part 4d in the discharging hole 4 is not touched to the tip part 4c at the outlet side. Therefore, as the remaining material 1 is not stuck to the tip part 4c at the outlet side, the discharging hole 4 can smoothly be closed with the closing cover 5 after discharging.