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• The double influence function method including flattening deformation influence function and deflection deformation influence function are established and combined used to solve the deformations between the rolls. • A model,considering the dispersion distribution characteristics of backing roll,for calculating the contact pressure between the rolls of the Sendzimir 20-high mill based on the double influence function method is established. • The conjugate gradient method is used to solve the contact pressure between the rolls by combining the force balance equation, the moment balance equation and the deformation compatibility equation group of rolls system. • The solving accuracy of the model established is consistent with that obtained by finite element method and the computation time can be greatly reduced. This paper established a model for calculating the contact pressure between the rolls of the Sendzimir 20-high mill based on the influence function method with considering the dispersion distribution characteristics of backup rolls. Stone's and Hirschcock's formula are used to calculate the rolling force between the work rolls and the rolling stock. The force balance equations and the moment balance equations of the roll system are established to determine the relationship between the contact pressure of rolls and the rolling force. The deformation-compatibility equation is established by combining the flattening deformation, deflection deformation, and rigid displacement of the rolls and roll crown. The influence function method is used to solve the flattening deformation and deflection deformation between the rolls. The conjugate gradient method is used to solve the contact pressure between the rolls by combining the force balance equation group, the moment balance equation group, and the deformation compatibility equation group of the roll system. The contact pressure between rolls obtained by the model established is compared to that by the finite element method. The results show that the calculation accuracy of the model established in this paper is consistent with that of the finite element method. Significantly, the contact pressure between the backup roll and the second intermediate roll can be accurately calculated by considering the dispersion distribution characteristics of the backup roll, and the computation time can be greatly reduced. [ABSTRACT FROM AUTHOR]