In this investigation, the "archipelago" design is presented as a platform for skin-mounted wearable and stretchable electronics. The electronic components of the design were distributed between islands connected by stretchable serpentine structures. The analytical results show that at 20% overall elongation, the serpentines stretch 60% due to the rigidity of the islands. This 20% elongation is defined as the system stretchability. The 60% elongation on the serpentines is defined as the effective stretchability. At 60% effective stretch, the calculated equivalent plastic strain in a serpentine interconnect is 0.67%, which is well below the fracture limit of copper. Elongation experiments show that the archipelago structure has the system stretchability up to 76% for one-time-stretching, translating to 228% of the effective stretchability on the serpentines. Fatigue-tension experiments show that at 20% system stretch, the archipelago structure can withstand on average 71,950 cycles without electrical or mechanical degradation.