Objective To derivate the paperboard constitutive model in the z-direction by compression and bending based on related literature and tests. Methods The stress-strain curve for z-compression was described by a Ramberg-Osgood function, and unloaded by a porous material model according to characteristics of the internal structure of the cardboard. The stress -strain relationship for band was described by composite laminates model and network model, and it was based on the paperboard of bending deformation processes. Results The model was able to describe the paperboard in the z-direction of the mechanical properties. It provided reference for the establishment of paperboard mold, and provided theoretical basis for finite element simulation of deformation in the z-direction of paperboard.