Deformation of flexible vesicles suspended in a fluid medium due to an applied electric field can provide valuable insight into deformation dynamics at a very small scale. In an electric field, the response of the vesicle membrane is strongly influenced by the conductivity of surrounding fluid, vesicle size and shape, and the magnitude of applied field. We studied the electrodeformation of vesicles immersed in a fluid media under a DC electric field. An immersed interface method is used to solve the electric field over the domain with conductive or non-conductive vesicles while an immersed boundary method is employed to solve fluid flow, fluid-solid interaction, membrane mechanics and vesicle deformation. Initial force analysis on the membrane surface reveals almost linear influence of vesicle size, but the vesicle size does not affect the long-term deformation which is consistent with experimental evidence. Highly nonlinear effect of the applied field as well as the conductivity ratios inside and outside of the vesicle are observed. Results also point towards an early linear deformation regime followed by an equilibrium stage for the membranes. Modeling results suggest that electrodeforming vesicles can create unique external flows for different conductivity ratios. Moreover, significant influence of the initial aspect ratio of the vesicle on the force distribution is observed across a range of conductivity ratios.