Curved electrode electrostatic actuators have been shown to have the potential to manipulate microparticles at high speeds in viscous dielectric media. However, there are no multiphysics models that fully describe the mechanics of these actuators in viscous dielectric media. This work is the first step in the direction of describing the actuator mechanics through Finite Element Method (FEM) simulations and validate it with the experiments. Simulations are performed using the commercial software Coventor MEMS+® and the results are found to be in good agreement with experiments. Two observations are reported in this study. One, for a given media and low actuator displacements, the cutoff frequency of the actuator is independent of the actuation voltage and/or actuator displacement. Two, an actuator immersed in a high viscous media will have higher squeeze film damping and a lower cutoff frequency. Through a simple lumped-parameter model of the actuator, we report that the viscous damping effect by the substrate on the actuator submerged in methanol or water media becomes significant for actuation frequencies >100 Hz.