In this paper we present a detailed computational study of an incompressible Newtonian fluid flow across a periodic array of two-dimensional cylinders which is a simplest non-trivial representation of a porous media. A twodimensional Lattice Boltzmann Method is used to solve the goving Navier-Stokes equation taking into account of viscous dissipation effects and influence of nonlinear fluid drag. Both the flow fields and the Darcy-Forchheimer drag coefficient as a function of the solid volume fraction are calculated for a wide range of flow Reynolds numbers. The predictions were compared with the results from conventional numerical and empirical models for verification. Apart from confirming that inertial effects can cause a significant deviation from Darcy’s law for large velocities the results also show that the characteristics of the vorticity field vary considerably as the Reynolds number increases, which will have major implications to the transport of passive particulate substances within the pores and their removal rate.