PURPOSE: To eliminate a partial thickness difference in a metallic tube and to prevent reduction in grinding efficiency by inserting a shape correcting device into the inside of a metallic tube previously, and grinding the outside face of the metallic tube after correcting a roundness defect and a curvature in the longitudinal direction.

CONSTITUTION: A metallic tube 17 is inserted into a shape correcting device 1, and a handle 15 is rotated, so that one of rotation driving members 10, 11 protruding from the end parts of the metallic tube 17, in other words, the rotation driving member 11 gearing with a screw 9 provided in the end of a shaft 2 is pushed into the tube 17. This pressing force is transmitted one by one to adjacent overhanging devices 3 via a pair of ring members 5, a coil spring 8, and a belleville spring 4 in the overhanging device 3, and a circular arc member 6 is pressed onto the inside face of the metallic tube 17 when a pair of links 7 rises against the spring 8. In this way, the shape of the metallic tube 17 is corrected, and after the shape correction, the handle 15 is removed, and then, the tube outside face is ground on a grinding line with leaving the shape correcting device 1 inside the tube 17.