ACE3P, a 3D massively parallel finite-element simulation suite that can perform integrated electromagnetic, thermal and mechanical analysis, is being developed at SLAC National Accelerator Laboratory for the past decades becoming an important tool for design and analysis of particle accelerators. Based on the finite-element framework of ACE3P, a new eigensolver is developed for modal analysis of mechanical structures. Running on massively parallel computer platforms, the new solver can handle large-scale problems by utilizing their computing resources and thus provides timeefficient capability to perform modal analysis of complicated accelerator components. This simulation functionality helps understanding the microwave response and feedback requirements of superconducting cavities to microphonics that can affect the operational reliability of a particle accelerator.