Managing the mechanical mismatch between hard conductor/semiconductor device components and soft biological tissues represents a key challenge in the development of advanced forms of wearable electronic devices. In this talk, I will discuss two mechanical design strategies to address this issue. The first strategy consists of producing a structure in which a liquid surrounds the electronics and resides in a thin elastomeric shell to provide a strain-isolation effect that not only enhances the wearability but also the range of stretchability in suitably designed devices. Combined experimental and theoretical results establish the strain-isolating effects of this system, and the considerations that dictate mechanical collapse of the fluid-filled cavity. Examples in skin-mounted wearable include wireless sensors for measuring temperature and wired systems for recording mechano-acoustic responses. In the second strategy, we strive to increase the stretchability of metallic interconnects on stretchable substrates. Finite element analyses reveal a substantial increase in stretchability with reducing substrate thickness. Low-cycle fatigue tests confirm this trend by examining the stretch required to form fatigue cracks associated with plastic deformation. To elucidate the mechanics governing this phenomenon, we examine the buckling behavior of deformed serpentine interconnects on substrates of various thickness. Our experimental and theoretical studies suggest a change in the buckling mode from local wrinkling to global buckling below a critical thickness of the substrate. The global buckling found in thin substrates accommodates large stretching prior to plastic deformation of the serpentines, thereby drastically enhancing the overall stretchability of these systems.