In the present work, numerical simulations of electrohydrodynamic (EHD) flows of conducting droplets were performed by implementing the leaky dielectric model in the computational fluid dynamics (CFD) software OpenFOAM. Electric field effects in conducting droplets of both Newtonian and viscoelastic fluids were studied, where the Giesekus constitutive equation was used to describe the viscoelastic behavior of the droplet. In all the cases, the surrounding fluid was considered to be Newtonian. The numerical results were compared with Taylor's analytical solutions for Newtonian fluids and the influence of the parameters of the Giesekus model on the deformation of viscoelastic droplets was evaluated. Simulations predicted both prolate and oblate deformations as well as the circulation patterns inside and outside the Newtonian droplet, which were consistent with experimental and analytical results. For the case of viscoelastic droplets, the deformation was found to decrease with increasing relaxation time and mobility factor. The droplet deformation was observed to be slightly higher when a solvent was included as compared to that when no solvent was considered. The droplet deformation is primarily influenced by the electric field magnitude; however, other parameters such as the conductivity, permittivity, and elasticity also play a role on the deformation magnitude. (C) 2014 Elsevier B.V. All rights reserved.