Although many modeling approaches exist for analyzing the behavior of capacitive micro-machined ultrasonic transducers(CMUTs),the relation equation between the design parameters with input and output is still lacking.What there is can only be used to analyze the dynamic performance of CMUT indirectly and qualitatively,such as stiffness and sound pressure.A lumped-parameter theoretical model based on the dynamic theory is proposed in this paper.The relation equations between the design parameters with inputs and outputs are given.The results obtained by the proposed model agree well with those by finite element method(FEM)simulation.The dynamic and static behavior of CMUT can be clearly depicted,which is helpful for design and optimization iterations.This shows that the proposed model makes it easier to optimize the parameters of a CMUT with respect to output and bandwidth directly and to better understand the influence of each parameter. Although many modeling approaches exist for analyzing the behavior of capacitive micro-machined ultrasonic transducers (CMUTs), the relation equation between the design parameters with input and output is still lacking. Where there is can only be used to analyze the dynamic performance of CMUTs and qualitatively, such as stiffness and sound pressure. A lumped-parameter theoretical model based on the dynamic theory is proposed in this paper. The relation equations between the design parameters with inputs and outputs are given. The results obtained by the proposed model agree well with those by finite element method (FEM) simulation.The dynamic and static behavior of CMUT can be clearly depicted, which is helpful for design and optimization iterations. This shows that the proposed model makes it easier to optimize the parameters of a CMUT with respect to output and bandwidth directly and to better understand the influence of each parameter.