The structure of paper obviously has a significant influence on end properties, such as its receptivity to ink. However, past models of ink penetration have usually referred primarily to the ink and the printing condition. To learn more of the influence of paper on ink penetration, a study was made in which the paper consisted of two bonded layers which could be separated after printing. Thus, the ink coverage at gradient levels within the sheet could be measured directly, providing equilibrium penetration factors. Unbonded layers were employed to study penetration at dwell. Correlation between the penetration factors and certain structural properties of the sheet, calculated from statistical geometry, showed the existence of complex relations. Paper structure considerations supported the estimation of realistic paper surface. It was possible from this, and the measured data, to determine the influence of three phases of penetration and verify the existence of substantial pressure penetration at dwell.