The work aims to carry out stiffness and modal analysis on parallel mechanism of 3UPS+1RPU in finite element method to find out weak link of mechanism stiffness and the resonance frequency regarding the special application requirement of carrying heavy objects and high working accuracy in the automatic packaging process. Firstly, the 3D model was established by SolidWorks software and then imported into Ansys Workbench for finite element analysis. The deformation cloud and stress cloud of the whole mechanism were obtained under two different forces at some working position. Through the modal analysis, the natural frequencies from first order to sixth order of 34.5, 35.8, 50.1, 523.9, 526.7, 528.8 Hz and the vibration mode of each order frequency of the 3UPS +1RPU parallel mechanism were obtained. It is concluded that the weak position of mechanism stiffness is discovered, proving that the static stiffness of the mechanism meets the design requirements. The resonance-prone position in the process of movement is found out, which can consequently avoid or suppress the resonance during the movement of mechanism.