The "island-bridge" mesh structure is widely adopted for flexible epidermal electronics to simultaneously achieve the electronic functions and mechanical flexibility. Mechanical intuition tells that the small size of the "island" is beneficial to the flexibility of the structure and the adaptability to complex geometric targets. Here, a plane-strain model and an axisymmetric model are established for square "island" and cycle "island," respectively, to analyze the mechanical system consisting of the flexible epidermal electronics and the human skin. It is found that the pressure between the "island" and the human skin is positive at the inner region and reaches a peak value at the center, while is negative at the outer region and approaches infinite at the boundary of the contact region. With the increase in the size a/R-0, the amplitude of the pressure significantly increases, as well as the singular degree of the pressure at the boundary. The reduction of the "island" size is beneficial for the optimization of the "comfort level" of the flexible epidermal electronics. The models degenerate into the famous Johnson-Kendall-Roberts (JKR) model for the limit case with extremely hard and thick "island."