The stability of a liquid jet subject to a transverse electric field is investigated in the framework of electrohydrostatic theory. It is shown that depending on the magnitude of permittivity ratio of the involved fluids S = ε i /ε o (inner to outer) compared to a critical permittivity ratio S cr ≈ 27.45 the jet exhibits distinct behaviors; for S < S cr the jet is stable and elongates indefinitely as the electric field is increased, while for S > S cr it shows hysteresis behavior and becomes unstable beyond a critical electric capillary number Ca cr . The results suggest that the jets are generally more stable than liquid drops.