A method of continuously casting a billet with a small cross section in which the billet has a cross sectional area of 700 cm 2 or less and a curved type or vertical type continuous casting machine is used while oscillating the mold upward and downward, wherein: the casting machine is provided with motors for driving pinch rolls at a speed corresponding to an aimed withdrawing speed and a mechanism for withdrawing speed oscillation, the mechanism has structural play in the directions of driving and reverse driving in such a manner that the amount of a play-incurred displacement from the neutral position of the structural play in the direction of driving the billet or reverse driving is 2-30 mm in the direction of driving and 2-30 mm in the direction of reverse driving, each on the pinch roll circumferential length equivalent basis; the drive of each motor is transmitted to the pinch rolls via the mechanism for withdrawing speed oscillation, whereby: the billet withdrawing speed during the upward period of mold oscillation becomes slower than the average withdrawing speed and faster during the downward period of mold oscillation than the average withdrawing speed; and operational parameters are set such that the casting speed is 1.5 m/min or more; the amplitude of oscillation in the + direction is 1.5 to 4.0 mm, the amplitude of oscillation in the - direction is 1.5 to 4.0 mm, and the frequency of oscillation is 450 cpm or less, characterized in that the operational parameters are further set such that the length of the billet from the meniscus to the site of cutting of the billet is 50 m or less, and the specific amount of secondary cooling water is 0.8 liter/kg of steel or less, and in that the mechanism comprises elastic parts either alone or in combination with dampers between the motors for driving the pinch rolls at a speed corresponding to an aimed withdrawing speed and the pinch rolls, and in that the mechanism further has a function such that the reaction force of the elastic parts for returning to the neutral position increases in response to the increase in the play-incurred displacement from the neutral position. the casting machine is provided with motors for driving pinch rolls at a speed corresponding to an aimed withdrawing speed and a mechanism for withdrawing speed oscillation, the mechanism has structural play in the directions of driving and reverse driving in such a manner that the amount of a play-incurred displacement from the neutral position of the structural play in the direction of driving the billet or reverse driving is 2-30 mm in the direction of driving and 2-30 mm in the direction of reverse driving, each on the pinch roll circumferential length equivalent basis; the drive of each motor is transmitted to the pinch rolls via the mechanism for withdrawing speed oscillation, whereby: the billet withdrawing speed during the upward period of mold oscillation becomes slower than the average withdrawing speed and faster during the downward period of mold oscillation than the average withdrawing speed; and operational parameters are set such that the casting speed is 1.5 m/min or more; the amplitude of oscillation in the + direction is 1.5 to 4.0 mm, the amplitude of oscillation in the - direction is 1.5 to 4.0 mm, and the frequency of oscillation is 450 cpm or less, characterized in that the operational parameters are further set such that the length of the billet from the meniscus to the site of cutting of the billet is 50 m or less, and the specific amount of secondary cooling water is 0.8 liter/kg of steel or less, and in that the mechanism comprises elastic parts either alone or in combination with dampers between the motors for driving the pinch rolls at a speed corresponding to an aimed withdrawing speed and the pinch rolls, and in that the mechanism further has a function such that the reaction force of the elastic parts for returning to the neutral position increases in response to the increase in the play-incurred displacement from the neutral position.