A computational method was developed to determine the correlation between permeability and the Forchheimer (non-Darcy) coefficient and to investigate numerically the factors that affect this correlation. The method is based on the construction of a 2-D random pore network. The porous medium is represented as a network of cylindrical pipes with randomly generated size, orientation, and connectivity. Probability density functions are used to characterize the orientation, length, diameter, and connectivity properties of the pipes that form the pore space. In this article the development and validation of the computational method are discussed. The computational procedure provides an expected value for the medium properties and a variation around this expected value, which is a measure of the uncertainty associated with the calculation of porous media properties. It was found that the porous medium structure has a strong effect on the flow properties. Specifically, the splitting of the pores is mostly responsible for non-Darcy flow behavior. Examination of the behavior of the medium properties under compaction shows that there is a unifying correlation for the behavior of the permeability. However, each type of porous medium exhibits different non-Darcy flow behavior under compaction. Finally, a statistical model, which correlates the structure characteristics of the porous medium to the measured properties, is presented.