The quality of a wound roll is highly dependent upon the in-roll stress distribution, which is controlled by the operating parameters of center torque, nip and tension. With increasing demands for higher performance of paper winding machines in terms of higher speed of winding, wider width of web and larger diameter of wound roll, it becomes of vital importance to determine the optimum operating conditions of the machines. In this paper, a new numerical formulation for paper winding is proposed taking account of the effect of nonlinearity in paper compressibility, air-entrainment and permeance. The proposed theory of winding is based on the assumption that the accumulation of the in-roll stress by a wound-on layer can be expressed as the superposition of the stress increment calculated from a mechanical model of a pressured thick cylinder. The theory of elastohydrodynamic lubrication with the compressibility of air is introduced to evaluate the effect of air-entrainment. Permeance of air is expressed under the assumption that permeance is proportional to the pressure difference of both sides of a paper. The numerical stress analysis of wound rolls shows the significant effect of the air-entrainment and permeance upon the in-roll stress.