Gantry robots are commonly used in the bonding operation after IC packaging in panel industry and semiconductor industry. During the bonding process, bonder moving and bonding movement result in vibration and misalignment to IC pins. To ensure the bonding stability of gantry robots in high precision and as a basis to improve mechanical design, in this research, bonding models were first constructed and sent to ANSYS Workbench software to carry out the finite element analysis. Static structure simulation computed the deformation and precision from the components when four bonders moved to different positions. Moreover, in this study, based on Castigliano's theorem that deals with strain energy of materials subjected to forces, simulation results were verified by carrying out theory derivation.