  By using dimension reduction and homogenization techniques, we study the
steady flow of an incompresible viscoplastic Bingham fluid in a thin porous
medium. A main feature of our study is the dependence of the yield stress of
the Bingham fluid on the small parameters describing the geometry of the thin
porous medium under consideration. Three different problems are obtained in the
limit when the small parameter $\varepsilon$ tends to zero, following the ratio
between the height $\varepsilon$ of the porous medium and the relative
dimension $a_\varepsilon$ of its periodically distributed pores. We conclude
with the interpretation of these limit problems, which all preserve the
nonlinear character of the flow.
