A hydrostatically coupled dielectric elastomer (HCDE) actuator consists of two membranes of a dielectric elastomer, clamped with rigid circular rings. Confined between the membranes is a fixed volume of a fluid, which couples the movements of the two membranes when a voltage or a force is applied. This paper presents a computational model of the actuator, assuming that the membranes are neo-Hookean, capable of large and axisymmetric deformation. The voltage-induced deformation is described by the model of ideal dielectric elastomer. The force is applied by pressing a rigid flat punch onto one of the membranes over an area of contact. The computational predictions agree well with experimental data. The model can be used to explore nonlinear behavior of the HCDE actuators.