Dielectric elastomer actuators (DEAs) with a typical sandwich structure of electrode-elastomer-electrode arrangement provide large deformation. DEAs outperform most large displacement actuators in terms of light weight, low cost, and high efficiency. The actuation mechanism of DEAs relies primarily on the electrostatic force or the Maxwell stress which is due to the reaction of material polarization in an electric field. By a dynamic nonlinear electromechanical continuum model implemented with the finite element method, the dynamic response of a homogeneous DEA is studied. Results show that the actuation magnitudes can be increased when the frequency of the applied electric field approaches to the eigenfrequency of the DEAs. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)