Dielectric elastomers (DEs) are the polymers capable of inducing deformation under electrical stimulation. When subject to a voltage across its thickness, the material reduces in thickness and expands in area. This paper presents a new method to analyze deformation and stress distribution response of the dielectric elastomer actuator (DEA) model under different applied voltage. An equal-biaxial pre-strained circular actuator model was built. The Yeoh strain energy potential and the collocation method are used for describing the large strain actuation response and stress distribution. The study in this paper has shown that: the stress and the stretch distributions in the passive region of the DE actuator depend on the radial distance from the center at the calculation point of the passive region and the magnitude of the applied voltage; with the same excitation applied voltage, we can get a larger deformation actuation by choosing an appropriate pre-stretch ratio; the influence of the non-ideal material has seriously affected the actual deformation of the DE actuators. This analytical model has a reference potential for the design optimization of high performance DEA systems and the model-based control of the DEA robot.