Recently, a type of flexible grippers with low power supply (0–5 V) has been designed and developed for grasping small but precision parts. In previous work, the authors manufactured a soft gripper whose actuating components are made of ionic polymer-metal composite (IPMC) materials; however, there is not a comprehensive model to analyze the complete mechanics for this IPMC gripper. Therefore, this paper provides a finite element method for analyzing its static mechanics characteristics in the state with maximal stress and strain (i.e., the gripper opening largest, including the IPMC deformation, stress, and strain). Further, these electromechanical coupling relationships can be simulated by using the piezoelectric analysis module based on ANSYS software. The simulation results show that the maximal tip displacement of IPMC strips can nearly reach their own free length, the maximal stress is 54 MPa in the center of copper electrodes, and the maximal strain is 0.0286 on the IPMC strip. The results provide detailed numerical solutions and appropriate finite element analysis methodologies beneficial for further research on the optimization design, forecast analysis, and control field.