AbstractA numerical method was developed for flows involving an interface between a homogenous fluid and a porous medium. The numerical method is based on the lattice Boltzmann method for incompressible flow. A generalized model, which includes Brinkman term, Forcheimmer term and nonlinear convective term, was used to govern the flow in the porous medium region. At the interface, a shear stress jump that includes the inertial effect was imposed for the lattice Boltzmann equation, together with a continuity of normal stress. The present method was implemented on three cases each of which has a porous medium partially occupying the flow region: channel flow, plug flow and lid‐driven cavity flow. The present results agree well with the analytical and/or the finite‐volume solutions. Copyright © 2008 John Wiley & Sons, Ltd.