PURPOSE: To improve the center segregation of a cast slab and to produce a sound product at high yield by squeezing the cast slab having the specific range of the solid phase ratio in the center part at the initial stage after starting the squeeze and thereafter, varying the solid phase ratio according to a specific equation to execute the squeeze.

CONSTITUTION: At the time of continuously squeezing the cast slab of a steel having 0.5 to < 1.0 the solid phase ratio at the center part by drawing out from a mold for continuous casting, the squeeze is executed at the position shown in the range of 0.5 to < 1.0 of the solid phase ratio (f's) in the central part at the initial stage after starting the squeeze. After passing the initial stage of the squeeze, the solid phase ratio (f's) is varied according to the equation f's=(fs/2)+0.5 and the squeeze is executed at the position showing the solid phase ratio (fs). Then, at the time of varying from the solid phase ratio (f's) to the solid phase ratio (fs), the solid phase ratio is desirable to vary by varying the casting speed of a cast slab. By this method, since the segregation ratio of carbon component at the center part of the cast slab is stabilized in the early time, excess negative segregation can be prevented over the whole length of the cast slab.