A theoretical response of an electrostatic gap-closing actuator based on parallel plates to constant and low-frequency accelerations has been derived as a function of the applied acceleration and voltage. The nonlinear equation of motion is obtained in a dimensionless form from the fact that the inertial and damping forces are neglected at a frequency much less than the resonant frequency of the parallel plate, and thereafter the nonlinear equation is solved for the stable inter-plate gap at the acceleration and voltage. From the derived solution, the pull-in acceleration is obtained as a function of the applied voltage, and the pull-in voltage is also expressed as a function of the acceleration. The closed-form solution is validated by comparison with a numerical solution. The theoretical solution is in excellent agreement with the numerical results when the actuator is exposed to a constant acceleration as well as a low-frequency acceleration. The theoretical solution and pull-in acceleration and voltage thus provide guidance to prescribe operational constraints for devices that use the parallel plate actuator and to predict the response of the electrostatic gap-closing parallel plates to constant and low-frequency acceleration.