A continuous casting apparatus for steel comprising: a casting mold for casting a molten steel, which includes a pair of long side walls (3a, 3b) and a pair of short side walls (4a, 4b); a submerged entry nozzle which discharges the molten steel into the casting mold and is adapted to have Ar gas blown thereinto; an electromagnetic stirring device (7a, 7b) which is disposed along an external surface of each of the long side walls (3a, 3b) and stirs an upper part of the molten steel within the casting mold; and a pair of back plates (5a, 5b) disposed along the external surface of each of the long side walls (3a, 3b), wherein a curved portion (11a, 11b) which is convexly curved toward the electromagnetic stirring device (7a, 7b) in plan view is formed at least at a position where the curved portion (11a, 11b) faces the submerged entry nozzle on each of the long side walls (3a, 3b), and each of the long side walls (3a, 3b) including the curved portion (11a, 11b) has a uniform thickness, wherein the continuous casting apparatus is adapted to form a meniscus of the molten steel in a range H from a lower end portion of the electromagnetic stirring device (7a, 7b) to a position higher than an upper end portion of the electromagnetic stirring device (7a, 7b) by 50 mm when viewed along a vertical direction, and a shortest horizontal distance L between a top which is a most depressed position when an internal surface of the curved portion (11a, 11b) is seen in plan view and an outer peripheral surface of the submerged entry nozzle is 30 mm to 80 mm in the range H, wherein a depression depth D (mm) of the curved portion (11a, 11b) at the position of the meniscus is 5 to 50 mm, and wherein groove-like flow channels are formed on internal surfaces of the back plates (5a, 5b). a casting mold for casting a molten steel, which includes a pair of long side walls (3a, 3b) and a pair of short side walls (4a, 4b); a submerged entry nozzle which discharges the molten steel into the casting mold and is adapted to have Ar gas blown thereinto; an electromagnetic stirring device (7a, 7b) which is disposed along an external surface of each of the long side walls (3a, 3b) and stirs an upper part of the molten steel within the casting mold; and a pair of back plates (5a, 5b) disposed along the external surface of each of the long side walls (3a, 3b), wherein a curved portion (11a, 11b) which is convexly curved toward the electromagnetic stirring device (7a, 7b) in plan view is formed at least at a position where the curved portion (11a, 11b) faces the submerged entry nozzle on each of the long side walls (3a, 3b), and each of the long side walls (3a, 3b) including the curved portion (11a, 11b) has a uniform thickness, wherein the continuous casting apparatus is adapted to form a meniscus of the molten steel in a range H from a lower end portion of the electromagnetic stirring device (7a, 7b) to a position higher than an upper end portion of the electromagnetic stirring device (7a, 7b) by 50 mm when viewed along a vertical direction, and a shortest horizontal distance L between a top which is a most depressed position when an internal surface of the curved portion (11a, 11b) is seen in plan view and an outer peripheral surface of the submerged entry nozzle is 30 mm to 80 mm in the range H, wherein a depression depth D (mm) of the curved portion (11a, 11b) at the position of the meniscus is 5 to 50 mm, and wherein groove-like flow channels are formed on internal surfaces of the back plates (5a, 5b).