In this article, a v2f model is employed to conduct a series of computations of incompressible ow in a periodic array of square cylinders simulating a porous media. A Galerkin/least-squares finite element formulation employing equal order velocity-pressure elements is used to discretize the governing equations. The Reynolds number is varied from 1000 to 84,000 and different values of porosities are considered in the calculations. Results are compared to the available data in the literature. The v2f model exhibits superior accuracy with respect to k-e results and is closer to LES calculations. The macroscopic pressure gradients for all porosities studied showed a good agreement with Forchheimer-extended Darcy's law in the range of large Reynolds numbers.