super crown shape of the steel plate in the subsequent steps of cold rolling for this purpose according to the apparatus of the present invention as shown in fig3 the rolls of the rolling mills at least those used for the steps of hot rolling are formed in a concave a drum shape such that the thickness ratio of the central portion to the edge portions of the steel plate shaped by the rolls of the roughing mill is approximately 1 1 or greater and such that the relationship cc c h t c t h is satisfactory in the subsequent rolling mills wherein c c the thickness ratio of the central portion to the edge portions of the steel plate on the inlet side of the rolls c h the thickness ratio of the central portion to the edge portions of the steel plate on the outlet side of the rolls t c the thickness of the central portion of the steel plate on the inlet side of the rolls t h the thickness of the central portion of the steel plate on the outlet side of the rolls fig5 shows the shape of the rolls of each of the rolling mills which is most effective for imparting the super crown shape to the steel plates fig5 shows the case when the steel plate is rolled using rolls having initial crowns of concave dissimilar sizes ccw i e having rolls of drum shapes with dissimilar recesses of the mills r 4 f sub f 2 f 3 f 4 f 5 f 6 and f 7 the case when the steel plate is rolled using rolls having dissimilar rolling gaps sc i e using rolls.