Single-crystalline GaAs ribbons with thicknesses in the sub-micrometer range are fabricated with well-defined "wavy" (top) and "buckled" (bottom) geometries (see figure and inside cover). The resulting structures, on the surface of or embedded in an elastomeric substrate, exhibit reversible stretchability and compressibility to strains > 10%, more than five times larger than that of GaAs itself. By integrating ohmic and Schottky contacts, high -performance stretchable electronic devices (e.g., metal semiconductor field-effect transistors') can be achieved.