The linear stability analysis of dielectric liquid placed in uniform electric field with respect to perturbations of density of an initially uniform state was carried out. The electric field increases the instability increment for the stratification along the field and decreases it for the transversal stratification. Thus, anisotropic separation into liquid and vapor phases is possible in high electric fields for a liquid that is initially in unstable state, as well as in metastable or stable states. Computer simulations of electrohydrodynamics confirm the theoretical calculations. It is important that new regions of low density phase appear as narrow cylindrical channels oriented along the field. This mechanism of generation of gaseous phase in locally high electric field can play a key role in processes of inception and ultrafast propagation of streamers during breakdown of liquid dielectrics in nanosecond range.