In this paper we use the boundary integral method to simulate the dynamics of a liquid drop levitated by electrostatic force. Our numerical code reproduces the Rayleigh limit, the Taylor limit and the stable equilibrium shape of a leviated drop obtained by previous authors. It also reveals the mechanism by which a levitated drop might breakup. Using this code, we have obtained the natural frequencies of the drop under various levitation conditions. We have also examined the effect of the electrostatic field on the resonant interactions between the modes. We found that the presence of the electric field enhances the modal interactions; modes which otherwise would not interact become coupled to each other. Calculations of the dynamics of a levitated drop under a time-periodic electric field indicate that the main resonance occurs when the frequency of the electric field is near the free oscillation frequency of the fundamental mode.