Stretchable electronic devices that exploit inorganic materials are attractive due to their combination of high performance with mechanical deformability, particularly for applications in biomedical devices that require intimate integration with human body. Several mechanics and materials schemes have been devised for this type of technology, many of which exploit deformable interconnects. When such interconnects are fully bonded to the substrate and/or encapsulated in a solid material, useful but modest levels of deformation (<30-40%) are possible, with reversible and repeatable mechanics. Here, the use of prestrain in the substrate is introduced, together with interconnects in narrow, serpentine shapes, to yield significantly enhanced (more than two times) stretchability, to more than 100%. Fracture and cyclic fatigue testing on structures formed with and without prestrain quantitatively demonstrate the possible enhancements. Finite element analyses (FEA) illustrates the effects of various material and geometric parameters. A drastic decrease in the elastic stretchability is observed with increasing metal thickness, due to changes in the buckling mode, that is, from local wrinkling at small thicknesses to absence of such wrinkling at large thicknesses, as revealed by experiment. An analytic model quantitatively predicts the wavelength of this wrinkling, and explains the thickness dependence of the buckling behaviors.