Using appropriate layout in the design of the stretchable electronics is very important, since the optimized layout is capable of making the electronic system stretchable and maintaining the electrical performance and structural reliability. In this paper, a unit cell model with periodic boundary condition is proposed to investigate the stretchability and optimize the structure of the stretchable electronic systems with the 2D "horseshoe" layout. Unlike the monotonous trends in the cases of the "wavy", "mesh", and 1D "horseshoe" layout, each impact factor (metal wire thickness, metal wire width, eccentric angle) has an optimized value for the stretchability to reach its maximum. To comprehensively investigate the influence of these impact factors on the stretchability, we employ the response surface method and obtain the quadratic response surface function to mathematically explore the relationship between these impact factors and the stretchability of interest. The response surface method proposes an optimal design of the 2D "horseshoe" layout for the maximum stretchability, which agrees well with the finite element simulations results. The findings here provide a more programmable scheme and can be useful in formulating designs for the stretchable electronic systems.