One of most common flow fields used in proton exchange membrane (PEM) fuel cells is the serpentine flow field. Diffusion (which is caused by concentration gradient) and convection (which is caused by pressure gradient) are two major transport mechanisms in the serpentine flow field. In the serpentine flow field, there is a pressure difference between two adjacent channels that leads to an under-land cross-flow through the porous media of the gas diffusion layer (GDL) from the higher pressure channel to the lower pressure channel. High under-land cross-flow rate leads to a high oxygen concentration under the land area and a high water removal capability, but it causes a high pressure drop at the same time. Most researchers use Darcy law in their modeling to predict the under-land cross-flow rate, and the inertial effect is neglected. At low velocity, the inertial force can be neglected, so the relation between pressure gradient and velocity inside the GDL is linear. However, the inertial force becomes important at high velocity, and the relation between pressure drop and velocity inside the GDL is no longer linear, so Darcy law is not applicable. Thereby, the modified Darcy Law which includes the inertial effect is developed. Non-Darcy effect is defined as the ratio of the inertial effect to the sum of the inertial effect and the viscous effect, and it is used as a benchmark for accounting the importance of the inertial effect. In this study, our numerical modeling applied Darcy law and modified Darcy law in the single serpentine flow field, respectively. When non-Darcy effect is no less than 5%, Darcy law over-predicts the cross-flow rate by more than 10% compared to the modified Darcy law. Criterions of the application range of Darcy law in the single serpentine flow field are found with the dimensional analysis as well. From the experimental results, Darcy law significantly under-estimates the pressure drop in the single serpentine flow field, which has narrow land, high permeability and high inertial coefficient.