Gold films on an elastomeric substrate can be stretched and relaxed reversibly by tens of percent. The films initially form in two different structures, one continuous and the other containing tribranched microcracks. We have identified the mechanism of elastic stretchability in the films with microcracks. The metal, which is much stiffer than the elastomer, forms a percolating network. To accommodate the large elongation of the elastomeric substrate, the metal network twists and deflects out of the plane but remains bonded to the soft substrate. Consequently, the metal film experiences only small strains and deforms elastically without suffering fatigue.