Stretchable displays represent a critical advancement in next-generation wearable devices, attracting attention for their potential to address numerous challenges. This study introduces a novel stretching approach for stretchable devices through a rotational membrane design. Patterned substrates offer significant advantages in process compatibility and device performance among various fabrication methods. The rotational patterned substrate easily enables structural modifications, while vacuum deposition facilitates precise deposition of thin-film encapsulations and organic light-emitting diode (OLED) layers. The resulting stretchable OLED (SOLED) with optimized Al₂O₃/SiO₂ nanolaminate/parylene-C-based multibarrier encapsulation demonstrates comparable luminance, current density, and operational lifespan to glass-based OLED devices. The innovative membrane rotation technique evenly distributes stress across the substrate, ensuring stability under high-strain conditions. Notably, the structure remained stable under a strain of 60%, exceeding twice the strain tolerance of previous designs. This approach addresses the strain fill-factor limitations observed in prior studies, achieving sufficient strain capacity for high-density displays. Consequently, SOLEDs with high fill-factors minimize non-emissive circuit areas, paving the way for high-luminance, reliable, and stretchable displays tailored for next-generation wearable technologies.