  We analyze the steady fluid flow in a porous medium containing a network of
thin fissures i.e. width $\mathcal{O}(\epsilon)$, where all the cracks are
generated by the rigid translation of a continuous piecewise $C^{1}$ functions
in a fixed direction. The phenomenon is modeled in mixed variational
formulation, using the stationary Darcy's law and setting coefficients of low
resistance $\mathcal{O}(\epsilon)$ on the network. The singularities are
removed performing asymptotic analysis as $\epsilon \rightarrow 0$ which yields
an analogous system hosting only tangential flow in the fissures. Finally the
fissures are collapsed into two dimensional manifolds.
