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This paper describes a new method for fabricating highly stretchable and robust electrical circuits. The circuits consist of liquid metal (eutectic gallium indium alloy, EGaIn) enclosed in elastomeric microfluidic channels. In particular, a microfluidic hybrid structure made of two types of elastomers (polydimethylsiloxane (PDMS) and Ecoflex (type 0030, Reynolds Advanced Materials) with different stiffness has been developed to improve the stretchability and mechanical stability of the circuits. These circuits can be flexed, twisted, and stretched up to 2.2 times of their original length l0. When we applied this stretchable circuit for radio-frequency antennas, the antennas exhibited no degradation in reflected power even after being repeatedly stretched to l = 1.50 l0 more than 100 times. This stretchability also allows the resonance frequencies of the antennas to be mechanically tuned around 1 GHz. The stretchable and robust circuits may be useful in reconfigurable and conformal structures, wearable sensors and large-area electronics, and other devices that must undergo large mechanical deformation.