Dielectric elastomers are capable of large deformation subject to an electric voltage, and are promising for uses as actuators, sensors and generators. Because of large deformation, nonlinear equations of state, and diverse modes of failure, modeling the process of electromechanical transduction has been challenging.  This paper studies a membrane of a dielectric elastomer deformed into an out-of-plane, axisymmetric shape, a configuration used in a family of commercial devices known as the Universal Muscle Actuators.