In this paper, the Method of Multiple Scales, and the Reduced Order Model method of two modes of vibration are used to investigate the amplitude-frequency response of parametric resonance of electrostatically actuated circular plates under hard excitations. Results show that the Method of Multiple Scales is accurate for low voltages. However, it starts to separate from the Reduced Order Model results as the voltage values are larger. The Method of Multiple Scales is good for low amplitudes and weak non-linearities. Furthermore the Reduced Order Model running with AUTO 07p is validated and calibrated using the 2 Term ROM time responses.