The lattice Boltzmann method is developed to simulate the pressure-driven flow and electroosmotic flow of non-Newtonian fluids in porous media based on the representative elementary volume scale The flow through porous media was simulated by including the porosity into the equilibrium distribution function and adding a non-Newtonian force term to the evolution equation The non-Newtonian behavior is considered based on the Herschel-Bulkley model The velocity results for pressure-driven non-Newtonian flow agree well with the analytical solutions For the electroosmotic flow, the influences of porosity, solid particle diameter, power law exponent, yield stress and electric parameters are investigated The results demonstrate that the present lattice Boltzmann model is capable of modeling non-Newtonian flow through porous media (c) 2010 Elsevier B V. All rights reserved