PURPOSE: To prevent the bent of a special-shaped extruded material from generating by cooling a thick wall part with a coolant just after extruding the extruded material consisting of a thick wall part and a thin wall part.

CONSTITUTION: The extruded material 3 is formed by a flat die 5 having a clearance of L-shape in the face view where a thick wall part forming clearance 7a is communicated into one end of a thin wall part forming clearance 7b. A coolant discharging hole 9 is provided adjacently to the thick wall forming clearance 7a, and the coolant such as liquefied nitrogen, nitrogen gas and air is blown and cooled on a thick wall part 1 of the extruded material 3. Because a thin wall part 2 of the extruded material 3 is yet in the softening state, the thermal contraction of the thick wall part 1 is not disturbed with the resistance of the thin wall part 2, and the extruded material 3 is extruded in the straight state. Further, in the cooling process of the extruded material 3, the difference of the thermal contraction action of the thin wall part 2 and that of the thick wall part 1 is made small, and the bent is suppressed or prevented. Accordingly, the stretch amount can be suppressed in the stretch process being succeeding to the cooling process.