This paper is concerned with formulating equations for the flow of an electrically conducting fluid through a non‐conducting porous medium with non‐porous and non‐conducting boundaries. Equations are developed for the general case of the flow of a solid‐fluid suspensions; flow through a porous medium is treated as a special case by letting the velocity of the particle phase goes to zero. Two cases are considered. Exact solution is obtained for the case of flow between parallel plates, but for flow in pipes of square and circular cross sections, the equations have to be solved numerically. The numerical technique developed can treat elliptical cross sections as well. The flow in all cases is assumed to be steady, laminar, incompressible, viscous, and fully developed. The results are presented in terms of a parameter which measures the resistance of the porous medium.