  We consider the standard first passage percolation model in the rescaled
lattice $\mathbb{Z}^d$ for $d\geq 2$ and a bounded domain $\Omega$ in $\mathbb
R ^d$. We denote by $\Gamma^1$ and $\Gamma^2$ two disjoint subsets of $\partial
\Omega$ representing respectively the source and the sink, i.e., where the
water can enter in $\Omega$ and escape from $\Omega$. A maximal stream is a
vector measure $\overrightarrow{\mu}_n^{max}$ that describes how the maximal
amount of fluid can enter through $\Gamma^1$ and spreads in $\Omega$. Under
some assumptions on $\Omega$ and $G$, we already know a law of large number for
$\overrightarrow{\mu}_n^{max}$. The sequence
$(\overrightarrow{\mu}_n^{max})_{n\geq 1} $ converges almost surely to the set
of solutions of a continuous deterministic problem of maximal stream in an
anisotropic network. We aim here to derive a large deviation principle for
streams and deduce by contraction principle the existence of a rate function
for the upper large deviations of the maximal flow in $\Omega$.
