Subject to an electric voltage, a layer of a dielectric elastomer reduces its thickness, so that the voltage induces a high electric field. The positive feedback may cause the elastomer to thin down drastically, resulting in an electrical breakdown. The authors show that the electromechanical instability occurs when the Hessian of the free-energy function ceases to be positive definite. Their calculation shows that the stability of the actuator is markedly enhanced by prestresses, agreeing with existing experimental observations. © 2007 American Institute of Physics.