Summary: We study the solution of a non-Newtonian flow in a porous medium which characteristic size of the pores \(\varepsilon\) and containing a fissure of width \(\eta_\varepsilon\). The flow is described by the incompressible Stokes system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index \(1 < r < + \infty\). We consider the limit when size of the pores tends to zero and we obtain different models depending on the magnitude \(\eta_\varepsilon\) with respect to \(\varepsilon\).