The rolls in contemporary four-high mills cannot be maintained parallel during the rolling process.Therefore,four-high rolling mill vibrations take place in six degree of freedom(DOF)leading to spatial behaviors involving vertical,horizontal,axial,torsional,cross and swinging vibration modes resulting in complex relative motions between the rolls.Two numerical methods,modified Riccati-transfer matrix method(Riccati-TMM)and finite element method(FEM),are presented to analyze a spatial vibration characteristic of two four-high rolling mills with different stability.The natural frequency and mode shape of four-high rolling mills are obtained,and the clearance has a great effect on natural frequency and mode shape.In addition,field testing experiment is also conducted to measure natural frequency by power spectrum analysis of rolling mill vibration.Experimental results basically agree with those calculated by Riccati-TMM and FEM,which means that the Riccati-TMM and the FEM can be used for analysis of spatial vibration of four-high rolling mill.Meanwhile,the spatial vibration shows more compound vibration behaviors and the negative effect of horizontal,vertical,cross and swinging vibration modes are effectively controlled after redesign of rolling mill.These advantages have a great significance for the rolling mill to be operated with a much higher rolling speed and improved yield of products. The rolls in contemporary four-high mills can not be maintained parallel during the rolling process. Before, four-high rolling mill vibrations take place in six degree of freedom (DOF) leading to spatial behaviors involving vertical, horizontal, axial, torsional, cross and swinging vibration modes resulting in complex relative motions between the rolls. Two numerical methods, modified Riccati-transfer matrix method (Riccati-TMM) and finite element method (FEM), are presented to analyze a spatial vibration characteristic of two four-high rolling mills with different stability. natural frequency and mode shape of four-high rolling mills are obtained, and the clearance has a great effect on natural frequency and mode shape. addition, field testing experiment is also conducted to measure natural frequency by power spectrum analysis of rolling mill vibration. Experimental results basically agree with those calculated by Riccati-TMM and FEM, which means that the Riccati-TMM and the FEM can be used for analysis of spatial vibration of four-high rolling mill.Meanwhile, the spatial vibration shows more compound vibration behaviors and the negative effect of horizontal, vertical, cross and swinging vibration modes are effectively controlled after redesign of rolling mill. for the rolling mill to be operated with a much higher rolling speed and improved yield of products.