AbstractThis paper develops the method of fundamental solutions (MFS) as a meshless numerical method to obtain solutions of two‐ and three‐dimensional slow Brinkman‐extended Darcy's flows. The solutions of the steady Brinkman equations are obtained by utilizing the boundary collocation method as well as the expansion of the fundamental solutions, which are derived by using the Hörmander operator decomposition technique. All the velocities, their partial derivatives, the pressure, and the stresses corresponding to the fundamental solutions are addressed explicitly in tensor forms. Two‐ and three‐dimensional Brinkman problems with Dirchlet and Robin boundary conditions are carried out to validate the proposed numerical schemes. Then, the method is applied to solve a peanut‐shaped problem and a joint flow of Stokes and Brinkman fluids. In the spirits of MFS, the proposed numerical scheme is free from singularities and numerical integrations and it also does not require any domain discretization. Copyright © 2007 John Wiley & Sons, Ltd.