The question of the behavior of the droplet in an electric field is a feed-back problem. The droplet shape determines the ponderomotoric force density pe caused by the electric field, and thus the electric field changes the equilibrium of forces at the droplet surface and influences the droplet shape. The mechanical sub-problem of the droplet shape and the electric sub-problem of finding pe are decoupled via an iteration in Sect. 2. After evolving both sub-problems stationary 3D and 2D results are given in Sect. 5. The problem is extended to non-stationary droplets in inhomogeneous electric fields in Sect. 6.