A flexible metal interconnect structure for transmitting signals between IC devices in flexible electronic devices is formed between two compliant flexible material layers that are laminated together form a multi-layer flexible substrate. The interconnect structure is formed by two rows of spaced-apart conductive pads (metal islands) attached to the inside (facing) surfaces of the flexible material layers. Compliant micro-contact elements such as micro-springs provide sliding metal pressure contacts that maintain electrical connections between the islands during stretching of the composite sheet. Specifically, at least two micro-contact elements are attached to each metal island in one of the rows, with one element in sliding pressure contact with an associated first metal island in the opposing row and the second element in sliding pressure contact with an associated second metal island. The islands and sliding contacts can be patterned into high density traces that accommodate large strains.