We introduce a new two-dimensional microscopic model for the simulation of non-Newtonian fluids. The model is based on the recently introduced lattice-gas and lattice-Boltzmann models of fluid dynamics, which simulate Newtonian fluids by simple interactions on the particle level. The model has the advantage of easy treatment of complex boundaries and multiphase fluids. We use the new model to study non-Newtonian flow in porous media, and find that flux is related to force by a simple scaling law. ¿ American Geophysical Union 1993