We modeled flexible microelectronic systems, in which a thinned silicon die is flip-chip bonded to a flexible substrate, and analyzed the stress and strain distribution generated during twisting deformation. Because of the presence of the rigid silicon die, the strain distribution of the system model was significantly different from that of the substrate model. Unlike the substrate model, there is no significant difference in the von Mises strain according to the position in both the molding layer and the substrate in the system model. Therefore, the results of modeling or testing only flexible substrate cannot be directly applied to predict the behavior of flexible microelectronic systems. The copper bumps revealed stress above the ultimate strength as well as the yield strength. Therefore, the copper bump would be the most mechanically weak component in the operation of the face-down flexible microelectronic system during twisting. By replacing copper bumps with polymer bumps, the maximum stress in the bumps can be significantly reduced from 282 to 47 MPa, and the maximum mechanically safe twisting angle was also improved from approximately 40° to 80°. Therefore, in flexible electronic systems where twisting deformation is applied, polymer bumps are a better bonding method than the conventional copper bumps.