A nonlinear anisotropic hypo-elastic continuum model is proposed to model at the macro-scale the mechanical response of paper sheets under biaxial plane stress conditions. The nonlinearity is introduced via a tangent Young’s modulus assumed to be a decreasing function of the maximum principal strain and dependent upon the difference between the average angle of orientation of the cellulose fibers population and the angle defining the maximum principal strain axis, to account for anisotropic effects. The continuum model parameters for macro-scale simulations are identified based on the experimental results on representative volume elements (RVEs) of plain paper tested under uniaxial tension. The same RVE data are interpreted according to a statistical micro-mechanics model, which incorporates the key morphological features of cellulose paper. As a result, a link between the macro-scale and the micro-scale models is established, and the micro-scale model can be called to provide further information on the status of fibers debonding and breakage at any point of the continuum along the deformation process. The methodology is validated in relation to paper specimens with an eccentric hole tested in tension.