This study constructs a two-dimensional axisymmetric finite element model (FEM) of the polymer-typed capacitive micromachined ultrasonic transducers (P-CMUT). The electromechanical FE model is created using the APDL programming technique. The ANSYS multiphysics solver with sequential approach and the Physics environment files are applied for the solution of the electrostatic-structural coupled-field analysis. Simulations are performed to investigate the operational characteristics, such as collapse voltage and the resonant frequency of the P-CMUT. The numerical results are found to be in good agreement with experimental observation. Having confirmed validity and accuracy of the proposed numerical model, the study of influence of each defined parameter on the collapse voltage and resonant frequency of the P-CMUT are also presented. To solve some conflict problems taken place in diverse physical fields, an integrated multi-objective design method involving electrical and mechanical characterization is developed to optimize the geometric parameters and material properties of the P-CMUT. The optimization search routine conducted using the genetic algorithm (GA) is connected with the commercial FEM software ANSYS to obtain the best design variable using multi-objective functions. The results show that the optimal parameter values satisfy the conflicting objectives of the design procedures, namely to minimize the collapse voltage while simultaneously maintaining a high resonant frequency. Overall, the presented results confirm that the combined FEM/GA optimization approach provides an efficient and versatile means for optimization design of the P-CMUT.