The polymer-based capacitive micro-arrayed ultrasonic transducers have been investigated using the finite element analysis. The ANSYS Multiphysics solver with sequential approach and the physics environment files are applied for the solution of the electrostatic-structural coupled-field problem. A 2-D electromechanical model is established to characterize the collapse voltage and the resonant frequency of the P-CMUT. Both the numerical and experimental results were in good agreement. An integrated multi-objective design method involving electrical and mechanical characterization was developed to optimize the geometric parameters of the P-CMUT. The optimization search routine conducted using the genetic algorithm (GA) is connected with the ANSYS model to obtain the best design variable. The optimal results show that the proposed approach provides another efficient and versatile numerical tool for multi-objective design and optimization of the P-CMUT.