Electric birefringence of unilamellar lipid vesicles, elongated in the direction of the applied field E, is modeled for a low degree of deformation to a prolate ellipsoid of the original spherical shells. The existing theory for water-in-oil microemulsion is adapted, and the intrinsic birefringence of the lipid membrane and the form birefringence of the aqueous inner compartment of the vesicle are taken into account. Deformation under both constant surface area and constant volume conditions are considered, but thinning of the bilayer at the polar caps and rotational/orientational effects are neglected. For illustration of the utility of the theoretical results, the extent of elongation of large unilamellar vesicles (LUV), prepared from the zwitterionic DOPC (dioleoylphosphatidylcholine), is calculated based on available experimentally measured induced birefringence data. With the use of reasonable values for the refractive indexes of the membrane, the axial ratio P of the deformed vesicle is found to be in the range of 1.02-1.07. The equations derived are also suitable for calculation of the bending elasticity modulus K of the bilayer from experimentally determined values of the Kerr constant K, provided the electrical and optical properties of the vesicle membrane are known.