The theory of hydrodynamic stability is useful in predicting transition between laminar and turbulent configuration for a given flow field i.e. hydrodynamic stability deals with predicting the most stable configuration for a given system and transition from laminar flow to turbulent flows as a natural progression of the system marked by the initial instability. One important problem in hydrodynamics is the impact of the electric field on the stability of two fluid systems. The discontinuity of the electric properties of the fluids across the interface affects the force balance at the fluid-fluid interface, which may either stabilize or destabilize the interface in question. There is increasing interest in the electrohydrodynamic stability as the electric field plays an important role in many practical problems of biophysics, chemical engineering and various other fields. In this book, the impact of electric field on the interfacial instability like Rayleigh-Taylor instability, Kelvin-Helmholtz instability has been presented. The effect of viscous irrotational stresses on the electrohydrodynamic stability has been formulated and solved.