The main objective of this thesis is to develop a mathematical model to characterize the static and dynamic behavior of a curved electrode electrostatic micro-actuator operating in an underwater environment. Such an actuation case involves the presence of multiple physical phenomena coupled together as a multi-physics problem to be solved by a combination of analytical and numerical methods. In this thesis, we derive a mathematical model as a continuous system using a reduced-order approach to characterize the motion of the actuator in response to step and sinusoidal input voltage waveforms. Our model accounts for the dielectric effects, inertial loading effects and squeeze film damping of the fluid media, and axial forces associated with mid-plane stretching of the beam electrode. We further simplified the model to achieve the case of parallel plate geometry and modeled the physical contact between the two electrodes at the pull-in phenomenon. We discretize both models by employing a Galerkin procedure and normalized modeshapes to find numerical solutions using MATLAB. We generated results for a few cases of actuation conditions in water, methanol and air media for both actuators and explored the effects of fluid properties on pull-in behavior. The curved electrode actuator only provided stable lower branch responses. To investigate the effects of fluid properties, namely, dielectric and viscous properties, we performed parametric studies on each actuator geometry with water as the medium. Our findings include that high dielectric properties and increasing voltages amplify the electrostatic force, causing faster (lower) pull-in times, while higher viscosity fluids cause higher squeeze-film damping, which slows down the (larger) pull-in times. We further simulated sinusoidal actuation voltage waveforms on both actuators and found that near pull-in, nonlinearities arise in the response, causing the excitation of higher harmonics.