Deformation of a fluid drop, suspended in a second immiscible fluid, under the influence of an imposed electric field is a widely studied phenomenon. In this paper, the system is analyzed numerically to assess its dynamic behavior. The response of the system to a step change in the electric field is simulated for both perfect and leaky dielectric systems, exploring the influence of the fluid, interfacial, and electrical properties on the system dynamics. For the leaky dielectric case, the dynamic build up of the free charge at the interface, including the effects of convection along the interface due to electrohydrodynamic circulation, is investigated. The departure of the system from linear perturbation theory is explained using these dynamic simulations. The present simulations are compared with analytic solutions, as well as available experimental results, indicating that the predictions from the model are reliable even at considerably large deformations.