In order to study the electromechanical coupling characteristic of dielectric electroactive polymer, the force analysis of DEAP under electrical field was performed, and the nonlinear electromechanical constitutive model was presented by combing the hyperelastic theory. On the basis of the model, the mechanical behavior of circular actuator was discussed. The Yeoh form of DEAP constitutive equation, the equilibrium equations and the boundary conditions were given. Thus, the principal stretch ratio and principal stress in the membrane of DEAP actuator were obtained by solving the differential equations. At the same time, the influences of pre-stretch ratio, the area of active region and actuation voltages on deformation of actuator were analyzed. And the experimental results for deformation behavior of circular DEAP actuator under voltage actuation were consistent with the theoretical analysis results. It was found that the optimal pre-stretch ratio was 3～4. 