The effects of elastic property on the deformation and breakup of an uncharged drop in a uniform electric field are investigated theoretically using the second-order fluid model as a constitutive equation. Two dimensionless numbers, the electric capillary number (C) and the Deborah number (De), the dimensionless parammeters governing the problem. The asymptotic analytic solution of the nonlinear free boundary problem is determined by utilizing the method of domain perturbation in the limit of small mathcal C and small De. The asymptotic solution provides the limiting point of C above which no steady-state drop shape exists. The linear stability theory shows that the elastic property of fluids give either stabilizing or destabilizing effect on the drop, depending on the deformation mode.