Stretchable electronics can be used for numerous advanced applications such as soft and wearable actuators, sensors, bio-implantable devices, and surgical tools because of their ability to conform to curvilinear surfaces, including human skin. The efficacy of these devices depends on the development of stretchable geometries such as interconnection-based configurations and the associated mechanics that helps to achieve optimum configurations. This work presents the essential mechanics of silicon (Si) island-interconnection structures, which include horseshoe and spiral interconnections, without reducing the areal efficiency. In particular, this study demonstrates the range of the geometrical parameters where they have a high stretchability and cyclic life. The numerical results predict the areas that are prone to breaking followed by experimental validation. The figure-of-merit for these configurations is achieved by mapping the fracture-free zones for in-plane and out-of-plane stretching with essential implications in stretchable and wearable system design. Furthermore, this work demonstrates the mechanical response for a range of materials (i.e., copper, gold, aluminum, silver, and graphene) that experience the plastic deformations in contrast to conventionally used Si-based devices that represent the extended usage for advanced stretchable electronic devices. The detailed mechanics of these configurations provides comprehensive guidelines to manufacture wearable and stretchable electronic devices.