Abstract: Further discussed are the geometrical conditions of line contact between two surfaces of revolution on the basis of the study on four essential mathematical equations in the process of cross rolling,and also discussed are the mathematical equations derived from these conditions with which another surfaces of revolution can be solved when one surfaces of revolution is known. The geometrical models of cross rolling expanding mill and cross rolling reducing mill are studied using the derived mathematical equations so as to investigate the possibility of the realization of cross rolling reducing process.