Electronic systems that offer elastic mechanical responses to high strain deformation are of growing interest due to their ability to enable new applications whose requirements are impossible to satisfy with conventional wafer-based technologies. This article reviews the mechanics of stretchable inorganic materials on compliant substrates. Specifically, three forms of stretchable structures are reviewed. The first one is stretchable ribbon, which provides one-dimensional stretchability. The second is stretchable nanomembranes, which can be stretched in all directions. The last is a noncoplanar mesh design, which has the advantage of providing large stretchability up to and exceeding 100%. Mechanics models and their comparison to experiment are reviewed for these three cases. Such models provide design guidelines for stretchable electronics.