  Equip the edges of the lattice $\mathbb{Z}^2$ with i.i.d. random capacities.
A law of large numbers is known for the maximal flow crossing a rectangle in
$\mathbb{R}^2$ when the side lengths of the rectangle go to infinity. We prove
that the lower large deviations are of surface order, and we prove the
corresponding large deviation principle from below. This extends and improves
previous large deviations results of Grimmett and Kesten (1984) obtained for
boxes of particular orientation.
