Capillary penetration in a porous medium is analyzed mathematically by using a two-dimensional network model. In the model, a porous material is assumed to be a network which is composed of many cylindrical pore segment of different diameters and equal lengths. The theoretical liquid saturation in a granular bed is equal to 100% when the height of capillary rise is lower than almost the half of the equilibrium height. However, when the capillary rise is higher than almost the half, the saturation remains less than 100%, and decreases gradually with increasing of the height. This fact is confirmed in the experiments using a glass granular bed with water, kerosene and ethylacetate.