In this paper, we established an analytical model that avoids extensive numerical computation for the analysis of a hydraulically amplified dielectric elastomer actuator. This actuator comprises a thin elastomer shell filled with an incompressible dielectric fluid coupled with a pair of electrodes placed in the central area. Application of high voltage on the electrodes inflates the actuator due to the induced Maxwell stress that pressurizes the incompressible dielectric fluid. The lumped parameter model predicts the stable functional region and the snap-through instability in the actuator. The model was compared with multi-physics finite element models that considered both linear elastic and nonlinear Mooney-Rivlin materials. The proposed model showed good agreement in the estimation of the actuation strain and the hydrostatic pressure as a function of voltage when compared to the finite element results. The average error in the axial and radial actuation using the proposed analytical model and nonlinear FEM models was 1.62% and 3.42%, respectively. This shows the model strength in the estimation of the actuator states and the critical voltage to avoid snap-through instability, required in applications such as control algorithms.