We modeled flexible microelectronic systems and analyzed the stress and strain distribution assuming an international standard bending test evaluating flexible electronics. The flexible microelectronic system consisted of a flexible substrate, a thin silicon die bonded to the substrate using bumps, along with an underfill and molding layer. The highest stress values were found at the square silicon die corners under bending deformation. After rounding the die corners, the copper bumps were the weakest component in the system. When polymer bumps replaced copper bumps to improve the mechanical stability, the critical bending radius reduced from 13.5 mm to 8.0 mm, and the silicon die was again the most vulnerable component. When the die thickness decreased from 50 to 30 μm, the critical bending radius of the flexible system even decreased to 6.9 mm. Therefore, it is advantageous for mechanically reliable flexible microelectronic systems to bond thin silicon dies with rounded corners to a flexible substrate using polymer bumps.