For conventional flexible printed circuit board widely used in industry, jointing islands of electric components with polyimide-supported copper serpentine interconnects is an effective approach to ensure circuit stretchability. The stretchability of the interconnects varies significantly due to the soft elastomer encapsulating the interconnect, as the encapsulation essentially constrains the lateral buckling of the serpentine structure during stretching. Previous studies have indicated that thin encapsulation with a low Young’s modulus is required to maximize stretchability. However, extremely low modulus and thinness lead to the elimination of the encapsulation function, and the design criteria for maximizing stretchability while maintaining adequate modulus and thickness are still unclear. This study investigates the dependence of stretchability on encapsulation stiffness, an index that simultaneously considers modulus and thickness. The interconnects with core-shell and single-elastomer encapsulations, each with a different stiffness, were prepared. The relationships between the elongation to failure of the interconnect and the tensile and bending stiffness of the encapsulation were investigated through experiments and finite element method (FEM) calculations. The results indicate that the tensile stiffness is a more useful index in encapsulation design than the bending stiffness because the elongation to failure monotonically decreases as the tensile stiffness increases. The results also indicate that the required tensile stiffness to maximize interconnect stretchability, essentially making the interconnect almost freely deformable, ranges from 5 to 34 N/m when the interconnects use an 18-μm-thick copper and 50-μm-thick polyimide.