We report on the successful fabrication of stretchable microsupercapacitor (MSC) arrays on a deformable polymer substrate that exhibits high electrochemical performance even under mechanical deformation such as bending, twisting, and uniaxial strain of up to 40%. We designed the deformable substrate to minimize the strain on MSCs by adopting a heterogeneous structure consisting of stiff PDMS islands (on which MSCs are attached) and a soft thin film (mixture of Ecoflex and PDMS) between neighboring PDMS islands. Finite element method analysis of strain distribution showed that an almost negligible strain of 0.47% existed on the PDMS islands but a concentrated strain of 107% was present on the soft thin film area under a uniaxial strain of 40%. The use of an embedded interconnection of the liquid metal Galinstan helped simplify the fabrication and provided mechanical stability under deformation. Furthermore, double-sided integration of MSCs increased the capacitance to twice that of MSCs on a conventional planar deformable substrate. In this study, planar-type MSCs with layer-by-layer assembled hybrid thin film electrodes of MWNT/Mn<sub>3</sub>O<sub>4</sub> and PVA-H<sub>3</sub>PO<sub>4</sub> electrolyte were fabricated; when they are integrated into a circuit, these MSCs increase the output voltage beyond the potential of the electrolyte used. Therefore, various LEDs that require high voltages can be operated under a high uniaxial strain of 40% without any decrease in their brightness. The results obtained in this study demonstrate the high potential of our stretchable MSC arrays for their application as embedded stretchable energy storage devices in bioimplantable and future wearable nanoelectronics