An electrostatic model of the energy of the surface layers of a metal is shown to describe in detail complex phenomena of surface relaxation in clean metals. The model accounts for relaxation effects that go many layers deep, that have both parallel and perpendicular components and that show large variations from surface to surface of the same metal. The model adds a new physically plausible assumption to the simple electrostatic model previously proposed by Finnis and Heine, which increases the force binding each ion to its bulk position by an amount fixed empirically for each metal. The equilibrium configuration of surface layers is found by minimizing the energy with respect to rigid translations of ion nets in a fixed electronic background density. The many surface structure parameters thus determined fit low-energy electron diffraction data on six surfaces of bcc Fe and six of fcc Al well in almost all cases. © 1986.