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Stretchable conductors are critical building blocks for enabling new forms of wearable and curvilinear electronics. In this paper, we introduce a new method using the interfacial design to enable stretchable conductors with ultra-high conductivity and robustness to strain using three-dimensional helical copper micro-interconnects embedded in an elastic rubber substrate (eHelix-Cu). We studied the interfacial mechanics of the metal-elastomer to achieve highly reversible conductivities with strains. The stretchable eHelix-Cu interconnect has an ultra-high conductivity (∼105 S cm−1) that remains almost invariant when stretched to 170%, which is significantly higher than in other approaches using nanomaterials. The stretchable conductors can withstand strains of 100% for thousands of cycles, demonstrating remarkable durability for exciting potential wearable electronic applications.