The purpose of this study is to derive macroscopic equations of motion in saturated porous media for non-Newtonian Bingham fluids (i.e. fluids exhibiting a yield stress) based on conceptual microscopic models of the porous medium and on the fundamentals of fluid mechanics. The `capillary tubes' as well as the `resistance to flow' models, developed for the case of Newtonian fluids, are here modified to account for the effects of the yield stress. A generalized Darcy's law is derived and expressions are developed which can be used to predict the conductivity of a homogeneous porous medium. In addition, the minimum static head gradient required for the initiation of flow in the porous medium is predicted using these two models. The analytical results hereby obtained are consistent with the scarce experimental data available in the literature and provide the proper theoretical framework for their understanding.