An analytical model is proposed for the dynamic analysis of a homogeneously deformed dielectric elastomer actuator (DEA) with a standard sandwich structure. The equation of motion for the DEA is obtained by the Euler-Lagrange equation. Numerical results of the model are presented to show the vibration and oscillation behaviour of the system. Resonance phenomenon and damping effects are investigated. Results are discussed in comparison with those of the related topics in the literature.