PURPOSE: To form a slit for opening wide in a long stretching cylinder consisting of a laminate of mats of inorganic fiber without risk of application of any unreasonable cutting stresses.

CONSTITUTION: At a supporting cylinder 8 to be inserted in a hollow cylinder 1, the first cutting edge 13 is protruded in the direction of the normal C nearer the foremost part, and the second cutting edge 22 is installed protrusively in the normal direction from the machine table 12 while facing the back of the supporting cylinder in the symmetrical position, and a third cutting edge 30 is installed protrusively in the direction normal from the supporting cylinder in the further rear position, and a fourth cutting edge 38 is protruded parallel with the tangent being directed to the foremost phase of the second cutting edge from the third cutting edge. The supporting cylinder 8 is secured to the machine table 12 by a guide plate 11 passing through a slit, and the hollow cylinder is inserted to the supporting cylinder 8 and slide. Because the cutting edges are fed in the depth direction in different positions in the longitudinal and circumferential directions of the supporting cylinder 8, no cutting stresses are concentrated locally, and the hollow cylinder 1 is free from risk of deformation.