Stretchable electronics offer soft, biocompatible mechanical properties; these same properties make them susceptible to device failure associated with physical impact. This paper studies designs for stretchable electronics that resist failure from impacts due to incorporation of a viscoelastic encapsulation layer. Results indicate that the impact resistance depends on the thickness and viscoelastic properties of the encapsulation layer, as well as the duration of impact. An analytic model for the critical thickness of the encapsulation layer is established. It is shown that a commercially available, low modulus silicone material offers viscous properties that make it a good candidate as the encapsulation layer for stretchable electronics.