We solve the coupled problem of the shape of a droplet in an electric field. An artificial pseudo‐transient process leads to an iteration over the decoupled electric and mechanical sub‐problems. We discuss the numerical behaviour of the iteration and of both sub‐problems and we present new 3d results of deformed droplets. Further, the motion of uncharged droplets driven by a non‐vanishing total ponderomotoric force is approximated in a new way for a model of a realistically shaped insulator. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)