In order to obviate some of the difficulties with conventional numerical methods of visualizing flow fields in porous media, we employ here a Lattice Gas Automaton (LGA) scheme. This is a discrete, microscopic, dynamic system whose coarse-grained statistical properties satisfy the Navier-Stokes equations. The discrete nature of the LGA makes it particularly suitable for digital computer simulation, and for solving problems with complicated solid geometries and complicated boundary conditions. We implement LGA on a supercomputer to simulate two-dimensional flow through porous media modeled as arrays of cylinders, in both ordered (in-line and staggered) and disordered arrangements, for a porosity value of 0.774. The relationship between the pressure gradient and the mean flow is determined at Reynolds numbers of O(10) which cover both the linear (Darcy) and non-linear regimes. The effects of packing disorder and of lateral solid walls in redistributing the flow through the pores are also examined.