The commercial success of displays of various form factors has encouraged the research on stretchable displays to produce the next-generation form factor. Stretchable OLED displays for wearable and healthcare electronics must deform under high strain, which entails image distortion due to the mechanical interaction between the substrate and device. This study introduces a perforated structure on the hyper-elastic substrate to reduce image distortion under uniaxial tension. The behavior and the effect of the perforated substrate are analyzed by a digital image correlation experiment and finite element analysis simulation, thereby providing a design method to attenuate the image distortion of the stretchable display.