PURPOSE: To improve the shape and yield of a product by rounding the shoulder of a taper part formed at one end of the 1st intermediate roll into a circular- arcuate shape in a Sendzimir mill for cold rolling.

CONSTITUTION: One end of each of the 1st intermediate rolls 7, 7' of an Sendzimir mill is formed into an approximately circular-arcuate part 12, and the curve of part 12 is formed so as to be tangent to the straight line of the cylindrical part of roll 7, 7'. The rolls 7, 7' are moved in the axial directions by a proper amount each, to roll indirectly a steel strip through work rolls 8. A ratio between the minimum diam. D of the tip of said part 12 and the diam. D0 of the cylindrical part is made to be, D/D0=99.18W99.87%. Further, a ratio between the roll length L, from the contact point of the straight line of cylindrical part 7, 7' and the curve of circular-arcuate part to the tip of part 12, and the whole roll- length L0 is made to be, L/L0=25W48.6%.