The serpentine interconnect is a key component in implementing the island-bridge architecture for stretchable electronics. It has a simple structure and is easy to design and fabricate. However, its dimensions significantly influence the elasticity and are often limited by manufacturing constraints and available space. In this study, stretchability was enhanced by incorporating support patterns within the dimensional limits. The serpentine line width was optimized for the printing process, and various support patterns with different sizes and positions were introduced. Finite element analysis was conducted to evaluate how support patterns affect the magnitude and location of the maximum strain in the serpentine structure. A solid elliptical support placed at specific locations distributed the strain more evenly and reduced the maximum strain by up to 50%. Tensile tests of the screen-printed stretchable electrodes confirmed this trend, thereby demonstrating a stretchability improvement due to the use of the elliptical support pattern. This approach improves stretchability within a limited area without requiring additional processing steps.