A thin slab that is free of internal cracks is formed by reducing a continuously cast strand having a liquid core. The placement of the reduction rolls is controlled to effect a suitable amount of reduction. The methods effectively reduce bulging strain, as well as strain associated with reduction of the strand. As a result, total accumulated strain is reduced and a thin slab free of internal cracks can be manufactured at high speeds. The apparatus includes reduction blocks which are capable of shifting the rotation angle of an upper roller segment frame. Misalignment strain is reduced and the thickness of the strand can be changed without stopping the manufacturing operation.